Find a Denon AVR-3600/3600dts on eBay for around $200-$250. And, yes, you need the remote. Now go around and look at a few garage sales and thrift shops for some vintage Infinity or JBL speakers. L-100, L-112, RS-4,5,6000, etc. You will likely need about $30 for a foam surround kit so try to keep the speakers to as little as possible.
Run AC-3 5.1 with a front L&R and a phantom center (no center). Save up for some small rear speakers.
But trust me, this system will really rock the place and it will do what ask very, very well.