I think speakers are going to be the most critical choice if you're to fore-go the sub. I live in an apt too, so I know all too well what you're talking about (subs are a no-no and will get the cops called on you
). However, I don't buy that "too much" story, especially if you're talking about power. Skilled use of the volume knob and cool neighbors will help. Surprisingly, my small bookshelf computer speakers at an extremely low volume bother my neighbors more than the floor standers I have with a 200wpc power amp driving them at 'risky' volume levels. So that tells me acoustics are a factor. Try to keep your speakers near the outer apt walls, not inner walls.
I'm not sure how you're going to pull off a reasonable system w/ no sub at $400. I know you can get buy with 2-channel instead of 5/7.1. That's why I say speakers will matter the most, even if you have to drive them with a cheap receiver. Nice speakers can provide you with fantastic imaging, bass, and everything else. I'm going to recommend some starter systems advice that will allow you to expand your system when you get a little extra cash. Buy the best speakers you can afford. With no sub, look for a mid-sized to floor standing model. For example, Paradigm's older Monitor series would be great. They're getting old enough now they don't have much resale value, but I can assure you you'll be pleased with them until you're able replace them. I'm sure someone else will chime in with a rec.
Next, be choosy in your electronics. I think that in the long run, you'll eventually stay with receivers or go with separates. Some folks go with an integrated amp; they are similar to a receiver, with less annoying features, and usually better quality. I highly encourage separates because they are easier to buy, trade, & sell, not to mention they are of better quality; it's more of a modular approach with you being able to selectively replace parts of your system without having to ditch the entire command center altogether. A simple preamp like the Rotel RC-1070 will do just fine. I think it runs something like $350 new (check ebay). Add an amp and you're good to go!
I understand that money is an issue. It always is. But if you're careful to lay a solid foundation, the extra money you spend will pay off in spades over the long run. I purchased only used equipment while I was in college. Receivers had to work for me because I couldn't afford separates. So just think of it like this: from now on, think of every purchase as an investment. Make smart purchases--this involves patience--just waiting for what you want to show up for sale or finding the best alternative. If you're not sure on something, then sleep on it or do more research. Don't be impulsive. And deal with someone that understands your need to not annoy your neighbors and will let you return things.