The budget is kind of low, but good enough for a "basic" system. I would suggest not to waste your effort on rear speakers early on. Get your self nice front speakers (components), subwoofer(s), and a 4-channel amplifier to drive that. The rear speakers, unless used with surround sound processing, only confuse the front stage anyways.
I would recommend this:
Precision Power Phantom P900.4 4-channel amplifier. It's relatively small and powerful. If you hurry up and buy one right now, get one from
sonicelectronix using PPI10 coupon code. That will drop the price to $180. I can't imagine a better value at this price. Use two channels to drive front speakers. That's 2x140watts RMS power. Bridge the rear channels. That will give you 450watts at 4ohms. That's enough to drive a lot of decent subwoofers. For the front speakers, there are a lot of options. For example, Massive Audio CK6V or Image Dynamics CTX (under $180 a set). I would recommend Hybrid Audio Unity if you can go over budget. If you can fit a single 12 inch subwoofer, just get one of those instead of two crappy 10 inch subs. One Image Dynamics IDQ12v3 should work nicely in a 1cu ft sealed box. Woofersetc offers one for $220 right now. It's a ridiculous value. This subwoofer has been a long time forum favorite on for SQ installs, and with 18 inches of one way linear excursion, it should get pretty loud too. If sealed box proves not to fit your tastes, build a ported box later on. If you want a cheaper subwoofer, Image Dynamics ID could work nicely. Of course, there are many other decent sounding subs for under $200. The key is to find one that works for your install. (e.g. with PPI amp, you have to have sub that can be wired for 4ohm load, and with good enough sensitivity to need 450watts or less to sound good).
And then there is the basic stuff. Wiring: get a quality 4awg or better power wire. If you buy a kit, make sure it comes with at least 100amp fuse. Sound proofing: it's essential to sound proof your front doors to improve the bass output of front speakers and to reduce rattles. I would prefer to use raammat products. Their web site also has a good tutorial.