The following systems are way under your budget, and I'm not sure if you need a blu-ray player with what your looking for too, but most of these systems are under $300. You can buy the Blu-ray player separate for $80-$100.
Onkyo HT-S3500 5.1-Channel Home Theater Speaker/Receiver Package
Sony BRAVIA DAV-DZ170 Home Theater System
Philips HTS3564/F7 Philips 3D Blu-Ray 5.1 Home Theatre System
Sony BDV-E3100 5.1 Channel 3D Blu-ray Disc Home Theater System with Built-In Wi-Fi
A Blu ray player adds very little cost, so I consider it worthwhile. The main reason I got one is that Redbox is often out of the DVD of a new release - but almost always has a BR disc available.
I do recommend that you get a separate BR player and receiver rather than an "all-in-one" system. While a receiver and speakers will last quite a while, a DVD or BR player will die well before your receiver.
I suggest that for most viewers the receiver won't be the weak link. Denon, Pioneer, Onkyo. All solid build and design. Sony if you stay away from the lowest end. The speakers are going to be key to accurate reproduction and chair rumblin...if that is what you want. To be honest many people do not know the difference between a $500 home theater system and a $500 subwoofer. OR they don't have a room large enough to support a big system. Great sound can be experienced from smaller non-Bose systems. If possible, avoid plastic enclosures on the speakers. wood or particle board (aka MDF) with a faux wood finish will sound much better. Listen if you can.