What features are important or of note? What are appropriate prices to pay? Are there specific brands which provide a clear advantage over others?
You are likely going to get some opinionated comments and answers in response to this question. There are lots of good brands (frames and complete bikes) from all over the world. There are more and more options showing up in local bike stores, so if you can it will be best to go have a look. Even if you choose to purchase online, having spent some time looking at physical hardware will help you make your decision.
I'm going to make an assumption that you're asking about a fixed gear bicycle for road use as opposed to a track.
If you haven't read Sheldon Brown's detailed article then please do, it's a great place to start. Without reiterating all of the detail in that article I'll simply point out a couple of highlights:
The number one thing that you should look for is a brake. Again, others may offer dissenting opinions on this, but riding a fixed gear bicycle on the road without a brake is extremely dangerous.
Chain tension mechanism. You will have to be able to tension the chain on your fixed gear bike as it lacks the derailleur and pulley mechanism that handles that task on traditional geared bikes. This will likely be accomplished by means of horizontal rear wheel dropouts within which the wheel moves back and forth for adjustment. You may also encounter models with an eccentric bottom bracket mechanism. These typically add some weight and may be of less interest to you unless you happen to go for a rear disk brake (in which case moving the rear wheel to adjust chain tension is not an option)
If you are new to the world of fixed gears then you may be interested in having an option to run a freewheel as well. A flip-flop hub can offer the best of both worlds in that you can ride fixed or flip the wheel around and ride with a freewheel. This adds a small weight penalty and absolutely requires that you install a brake of course.
As for price, brands, geometries, gear ratios, frame materials etc. this is very much personal preference and the rules are the same as for any bicycle. You can typically splurge a little on a fixie because there are far fewer other components that you have to purchase and maintain.
I would break it down into the following categories...
conversions (road-bike that has been made into a fixed gear, practicable on bikes with horizontal drop-outs). Pros: cheap, Cons: getting chainline right can be a bitch, not worth it for anything better than ghetto.
road-like (slack angles more like a road bike, wide-ish tires are possible, front/rear brakes standard, water bottle mounts exist). Example: Surly Steamroller Pros: rideable for long distances, Cons: Comfort of a roadbike with all the disadvantages of a fixed gear, bikesnobNYC will make fun of you.
track-like (aggressive angles like track bikes, large drop, usually only front brake, no ammenities, steel or aluminum, sometimes carbon fork). Example: Felt TK3, Bianchi Pista Pros: You can actually takes these on velodrome (w/o brakes) and not be laughed at. Cons: Impractical for non-pristine road conditions.
actual track bike (usually sold as frame/fork combo because you already have the wheels and cranks from your previous crash, alu or carbon w/carbon fork, no brake hole on fork, rear wheel is always "shoved under" seatpost). Example: Bianchi Super-pista, blue, etc Pros: This is the real deal, Cons: Really only worth it for a velodrome.
Here's the difference between a track bike and a road bike in terms of geometry. What this translates to in terms of handling will take some writing...
Track bike geom (Bianchi super pista)
AS 490 510 530 550 570 590 610 BS 515 525 535 550 560 575 585 B1 523 525 535 550 560 575 585 C 380 383 383 383 383 383 383 E 100 100 115 135 155 170 190 G 76 76 75.5 75.5 75.5 75 74.5 G1 74 74 74 74 74.5 75 75
Road bike geom (Bianchi Vigorelli)
AS 490 510 530 550 570 590 610 Bl 508 525 535 550 560 575 585 BS 510 515 525 542 553 569 578 C 408 408 410 415 415 415 415 D 58 68 68 68 68 68 68 E 115 125 135 145 160 175 195 F 580 584 585 591 602 607 612 G 74.5° 74.5° 74° 73.5° 73.5° 73° 72.5° Gl 71° 71° 71.5° 72° 72° 72.5° 72.5°
From my riding style and my delightful experience with my converted old steel 10 speed, what I like most in my bike is:
- Relatively lightweight;
- Narrow straight handlebars with always-ready-to-reach brake lever;
- Very "crunching" dual-pivot front brake caliper (generic brand);
- Very nice fit for my body-size;
- Decent crankset with steel chainring (very important to me!);
- No rear brake;
- 23mm tires.
Now the explanation: I use this bike for training and fair-weather commuting. I prefer it over my heavier bike (with fenders, lights, internal-geared-hub, rack) because it is so much faster (for being lighter), efficient (for having a simpler drivetrain and skinny tires) and nimble (for having a narrow handlebar and a trusty front brake). Being all-steel drivetrain (chainring, chain and sprocket), the chain oil keeps clean for much longer than with aluminum chainring, which makes the oil black too soon (and it stains the clothes a lot more!).
What I don't like in this bike:
- Headset bearing has a little play, very annoying and worrysome noises under full braking;
- Fork is of unknown origin. It seems fine, but the fork is for sure the most demanded mechanical part on this bike, since I don't skid, so all my braking goes on it;
- Front hub has quick-release skewer. I would rather not, because the ability to lock the bike away is more important, I think, than the ease of wheel removal (and fixies are very good for errands);
- Rear sprocket is low quality, so not perfectly centered. It is a pain down there, because I have to be sure the chain is not overtight, and even then there is one position where there is a small slack. It bothers while doing trackstands.
Well, I talked a lot, but I avoided to mention brands, I prefer to mention features, many good and pricey bikes might not have your desired features, and many apparently crappy bikes might have just what you need.
I bought one used and immediately spent 20% of paid price to replace some parts (crankset because of quality, stem and handlebars because of fit). That's the good part of fixies: you never need to spend a lot, since there is not so many parts to swap.
Hope it helps!