Your suburban riding scenario seems to call for a bike that would be a good "commuter" type bike on mixed city and suburban streets, with excellent hill-climbing abilities, and able to handle occasional brief "off road" ventures during a ride, e.g., riding through unpaved parking lots. The two primary suitable options would be hybrid/sport hybrid bikes and non-suspension mountain bikes. You could go the skinny tire "road bike" route, but I would only go there if you plan to go on group rides with groups that ride at road bike speeds, typically averaging 15mph or above on flat roads.
FIRST CHOICE, OPTION 1: "SPORT" HYBRID, aka "FITNESS" BIKE
I would recommend a "sport hybrid" type of bike with a somewhat upright riding position and low gearing for climbing hills, and one that has dropouts on the frame for attaching racks. Because of the hills, I also recommend hydraulic disc brakes, not cable discs, for best stopping power and safety. What's key here is that bike is equipped with discs; if it comes with cable-actuated discs, it's simple to replace the cable with hydraulic brakes for around $100 for a Shimano hydraulic brake set, just make sure to match to the size of the discs on the bike, e.g., 160mm discs. If you get a bike without disc brakes, it's likely it won't have the necessary frame dropouts to accept disc brakes; it's generally too expensive to try to retrofit a non-disc model to accept disc brakes.
Brands like Trek, Giant, Kona, Marin, Specialized, and others have numerous choices in this category; I personally chose a 5+ year old used Trek 7500 FX as my commuter, which was a rare 7500Fx model that had factory discs. The 7.5 FX model in Trek's current line, with discs, would be a good baseline comparison for looking at other manufacturer's hybrids. The Giant Escape 1 hybrid another poster mentioned would also fall into this general category and fits most of the criteria, but that model often may not come with disc brakes; for your scenario, I would avoid non-disc brake models.
CO-FIRST CHOICE, OPTION 1A: NON-SUSPENSION MOUNTAIN BIKE (29er)
You could also go with a 29er mountain bike, i.e., one with the 29-inch wheels, as long as you stay away from any sort of shocks and suspension (or at worst, front shocks with a lockout). Then simply equip it with road tires instead of knobby MTB tires; 32c width is a typical choice for a commuter bike.
The advantage of a 29er mountain bike for you is that they are highly likely to already come with gearing suitable for any hills you are likely to encounter. They are also highly likely to come equipped with disc brakes. Good name brand mountain bikes will also tend to be durable enough to stand up to a certain level of commuter abuse. This is also the type of bike that will be closest to "ridiculously heavy", but still probably lighter than your Chinese bike.
An example of an interesting 29er option would be the Northrock 29er mountain bike Costco sold for a while a couple years ago, if you could pick one up on Craigslist for $300 or so and swap on hydraulic brakes for $125 or so, and street tires, $50 or so/DOQ, you'd probably be very happy with that setup. IIRC correctly, the front shock has a lockout feature. I have one of those exact bikes I use as a mountain bike, and it's my best-feeling, fastest-riding mountain bike and my #1 bike for XC trails. I sold a similar Specialized 29er MTB I had because the Northrock rode faster and felt better for me.
OPTION 3: CYCLOCROSS BIKE
While I don't claim special expertise on cyclocross bikes, this type of bike could also be a fit for how you ride. Essentially they are ruggedized road bikes that typically come with hydraulic disc brakes. It's worth looking at some bike shops and asking them to show you cyclocross bikes.
OPTION 4: TOURING BIKE
It's also worth looking at bikes that are billed as touring bikes. There will be some overlap between these and Sport/Hybrid commuters. Touring-specific bikes will typically have more features to support carrying racks, camping gear etc. on the bike.
BRAKES
As I mentioned above, I am a big fan of the hydraulic disc brakes. You can typically stop the bike with a two-finger pull of the brake lever, even on a steep downhill. It's fine to buy a bike with mechanical discs, but for your own safety, absolutely upgrade the brake levers, lines and calipers with a hydraulic set, ASAP.
V-Brakes can work OK, but I feel safer, especially on hills, with the stopping power of hydraulic discs.
DRIVETRAIN
Personally, I would suggest a Shimano 9-speed rear drive train in this type of bike, because I don't see huge advantages of 10 and 11 speed drivetrains for commuter bikes. You could even go with 8 speed rear drive train; the Northrock bike I mentioned has an 8-speed drive train. 8 and 9 speed parts are readily available and good value and will be for years to come.
In general, for the front drive train, you will most likely want a bike with a "triple" crankset, i.e., 3 front gears/chainrings. The smallest chainring, on the inside, will be the one you will use when riding up steep hills. However, in newer bikes, many fitness models will come with a front "double" chainring and 10 or 11 speed rear drivetrain. These could be acceptable choices, but you'll have to pay more attention to gear ratios (and learn about things like "gear inches" to know for sure. Trek changed the 7.5 FX model to a double starting with the 2012 model year. (From 2012 on, the 7.4 FX model with discs still has a triple chainring and would be the baseline comparison bike)
GEARING
Other answers spoke to gear ratios; that's important, but I won't repeat that info here. If you went with the 29er mountain bike option, that would certainly have suitable gearing for climbing hills. In practice, a sport/hybrid will most likely have a suitable gear ratio too. Do get familiar enough with gear ratios so you can verify what works for you on the hills you ride.
The gearing you need depends on the steepness of the hill, most often measured in "grade". 10% grade is considered quite a fairly steep hill, and super-steep would be 20%. Sounds like you have hills of 10-20% grade. A 2010 Trek 7.5 FX front chainring has 26 teeth on the easiest front gear (lower # is easier), and a 26 teeth easiest rear gear. (higher # is easier in rear). A typical road bike, say, a 2010 Specialized Allez Elite, could have a 34 tooth easiest gear in front, and a 27 tooth easiest gear in the rear. The example Trek 7.5 FX is going to be a better, easier hill climber for you because of the easier gear in front, 26 front teeth for the Trek, vs. 34 front teeth for the Allez. The two bikes rear easiest gears are within 1 tooth (Trek: 26; Allez: 27) and there is a slight advantage to the Allez but nowhere near enough to offset the huge front chainring gearing advantage of the Trek, 26 teeth vs 34 teeth for the Allez. So the Trek will be the much easier climber than the Allez for steep, step hills, despite the Trek being slightly heavier at about 23 lbs compared to the the Allez at about 21 lbs.
With lower gears for hills, you'll need to "pedal faster!" but at a reasonable effort level. For example, you might have a pedaling cadence of 90 RPM at a "moderate-challenge" effort level, and wind up going uphill about 5 MPH, just a little faster than "walking speed". That's perfectly OK--you're steadily making it up the hill, without feeling like your heart is about to explode or feeling that you'll have to stop and walk the bike.
It's also worth mentioning that the length of the crank arm affects the difficulty of pedaling up a hill as well. Typical crank arms are 165-175mm long. I suggest using searching the web (including this site) for "gear inches" and learning how to calculate them, to compare different gear ratios and crank lengths. For gearing geeks there are online calculators at http://sheldonbrown.com/gears/ and http://www.gear-calculator.com/# that can help you compare different bikes.
To keep gearing simple: if you get a bike with a triple front chainring, you'll probably be fine on all your hills. If you are considering a bike with a double front chainring, then you will want to learn the gear inches calculations.
BE AWARE--GEARING CAN OFTEN BE EASILY CHANGED AFTER PURCHASE!!
Keep in mind... If you find a bike you otherwise love, that does not have low enough gears to climb your hills, often it's possible to install lower gears for a reasonable price. For example, a Shimano 9-speed drive train with 11-28t rear cassette gearing might be able to be swapped out with an 11-32t rear cassette, without changing any other parts. The 32t "low gear" could easily make all the difference for you on some hills. This is an "it depends" matter; consult a good bike mechanic (or ask here) with info on the specific bike and current drive train components, plus the gearing change you would like to make.
OTHER COMPONENTS
For your hilly commuter scenario, the options I mentioned should do well. It's possible to spend ridiculous amounts on wheels, upgraded drive trains, etc., but I don't think you need to, and you can upgrade as you go.
In general, on the sport hybrid bikes, if the parts are Shimano Deore, Sora, Tiagra, or comparable level parts, e.g., from SRAM, that's probably the a good place to be. For 29er mountain bikes, Shimano Alivio and above would be a good place to be.
SHIFTERS
In my opinion, there's no particular reason to care a great deal between grip shifters, and rapid fire (thumb lever type shifters). However, you will most likely be looking at bikes with the "rapid fire" type shifters in combination with disc brakes, and they are normally considered "higher end". So you may as well go with the flow and look for those types of shifters.
NEW OR USED
If you have a good idea of what you're looking for, you can find some great deals on good bikes on Craigslist and other sites. You can often find a bike that was built within the last 7-8 years that meets about all of what I laid out, and is in good condition, and is a great value. It can be a roll of the dice. However, find a good local bike shop, and even if a used bike you got has some issues, they often have excellent and friendly mechanics who will fix the issues at a reasonable price, where you still come out ahead.
If you find a new bike you like that meets what I laid out (or your more refined criteria) at a bike shop, absolutely, go for it. You're probably looking at bikes in the $600-1000+ price range.
FIT
If you buy new, a good bike shop will of course, fit you properly to the bike. In the used bike arena, you will need to learn-as-you-go the models, frame sizes and adjustments (e.g., matching seat height, handlebar angles, etc. to your body type, leg length, and riding style preferences) that fit you best. You can probably find a bike shop that will help you with fine-tuning fit adjustments on a used bike in the course of them doing other work on your bike. There are a lot of useful resources on bike fit on the Internet; use them and your local bike shops to make sure you get this part right for whatever bike you choose.
I hope that gives you some practical options for focusing your search. I recommend the Sport/Hybrid/Fitness type of bike as your overall best choice, and suggest as your starting comparison benchmark, using Trek 7.5 FX models from the last 5-7 years. Look at some of those, then look at similar models from other name brand manufacturers, Giant, Kona, Specialized, Marin, Cannondale, Fuji, and the numerous other brands that were originally sold through local bike shops. After looking at that category, you'll probably develop a pretty good idea of what you want, and can target a small set of used bike years/models/features, or buy a new bike that matches what you want. Good luck!
