When mine went out last winter I made copious use of blankets and a very cold rated sleeping bag (0? -10? -20? I forget the exact rating). That doesn't help with ambient, of course, but if a generator is not an option...
This is your answer. Forget the gas/liquid space heaters in an apartment. You can use them (illegally) to take the chill off for very short periods but it's more of a tease than anything. I don't think it's worth the hassle, danger, and expense.
It is nice to have something to heat up foods, like soup, coffee and tea. Do you have a gas stove--will it run without power? Just boiling some water will warm up the place dramatically but you don't want to try and heat the place with a gas stove because eventually the fumes can build up and kill you. Fill the largest pot of water you have and bring it to a boil every 4 hours.
Get whatever you'd use at least occasionally under normal circumstances. That's rule #1 for budgeting and practicality. You need experience with these gadgets.
If you're into camping, get a good sleeping bag and portable gas/alcohol stove.
If you hate camping get a couple wool blankets and some sterno fuel cans, which are cheap and can be used indoors, outside (for camping too actually), at parties, whatever. A gas grill (used outside) is good to have too if you're into grilling, which you can get them in tailgating size or full size of course.
AND a nice wool hat is priceless. 10 years ago when my apartment heat failed I slept like a baby with my wool hat, sweat pants, and a few blankets. I ran the faucets to a slow drip to prevent the pipes from freezing and it was so cold I had to break up the ice dams in the sink. but the pipes never did freeze and I was fine.
If you still have money to burn a good, portable generator is a luxury at $1k. The Honda ones are whisper quiet and again can be used camping--you see them in Boston all the time powering food carts and most people don't even know they're there. The cheaper generators will wake the dead so they won't work in an apartment situation.