I lack experience with entry-level (walmart, etc.) bikes, so take my answer with this in consideration. I was shopping this month for a good commuter bike to replace my old road bike (more about it below). I don't own a car, so I'll use it 15 miles per day, almost every workday between april and october, as well as for carrying all groceries and various errands.
From the opinions I got from bike shops I visited, the frame material is more a "performance" thing than anything - aluminium is lighter than steel/chromoly, but they'll all last forever. Steel is smoother on flat road, alu is enjoyable on hills. It's the quality of the components/groupset (derailleurs, etc.) that is driving factor in their recommendations: better components will last longer before needing adjustments (sooner) and repairs (later). How true is that, is hard to say for me, but I do think your budget should match the amount of milage you plan to do per year. My understanding is that walmart bikes are suited for a few hundred miles a year at most. You might do that well under 2 months if your bike is your main mode of transportation!
Take a look here for Shimano components comparisons in mtb/hybrids, where we see that SIS/Altus/Acera are considered recreational/sunday rides, while Alivio and Deore is where the better quality starts. From what I've heard, I wouldn't go below Alivio-equivalent, if you can afford it.
In any case, I suggest you get a little familiar with popular groupsets, frame types (steel, aluminium, etc.) and overall bike type (hybrid vs performance hybrid vs road) to get an idea of what you would want, and especially, make sure to take note of the models and bike sizes you try in bike shops! Then take a look at last-year sales for similar models (best period for this is april-may, unfortunately) or classifieds for the models that you like.
Anyway, for a commuter I'd steer clear of any type of suspension, disc brakes, wheels wider than 32C, grandpa sitting positions and large comfy seats, and look for compatibility with racks and fenders. Allow money for a helmet, lock, rear light, and possibly racks and bags (though you can use your backpack initially).
Don't forget the size of the bike is really important for long term comfort, so I'd suggest you get advice about this in a bike shop before even considering buying anything used/cleared!
With some knowledge, you will be able to assess walmart bargains better, and with some luck, you can land a used 300-500$ deal for a 600-700$ lightly-used bike you've just seen at the shop.
Finally, my personal anecdote: 10 years ago I felt I'd enjoy a more "serious" bicycle, and not just a teenager MTB. I bought a last-year model road bike (aluminium with Sora groupset which is entry level for road bikes) from a bike shop for around $700, which was a big deal for me back then. I used it for commuting, fun rides and occasional touring, and ended up doing at least 3K a year. Probably the best 700$ spent in my last decade, and looking back, a quite frugal, healthy and ecological investment compared to a purely utility wal-mart bike that by would likely have stayed inside after I would have gotten a car. So the question is: do you want to bike as a lifestyle now, or just as a means to get to work/school until you get a promotion? Your answer should help define your budget.
You do mention you don't have regular paychecks, so I would recommend to a) go to bike shops to get a sense of what you ideally look for, b) check clearances and classifieds, including walmart bargains c) if you don't find a great deal, make an informed decision on how much you're willing to spend.
