For headunit, what kind of features do you want? USB or aux input for an iPod or thumbdrive? Satellite radio? HD radio? Look at the Pioneer Premiere headunits, and pick one that fits your feature requirements and budget.
For your speakers, I suggest you start with a good set of component speakers for the front, with an suitable amplifier for them, and forget about rear speakers, at least for now. You'll get better imaging from the speakeres, and a good set of amplified speakers in the front will create plenty of sound, no need to add extra speakers in the back.
Generally speaking, component speakers will give you better sound than coaxials. They don't have to be expensive, either. You can get good sounding component speakers for as little as $90/pair shipped on
eBay (the PG RSd65cs).
For an amp, there are many options. It really depends on your speakers. Pick speakers, then pick an amp that provides enough power for your chosen speakers.
For subwoofer, yes you should get one. 6.5" speakers cannot reproduce the lower end of the audio spectrum, that's the subwoofer's job. I don't know a lot about good budget subwoofers, try browsing the subwoofer forum for recommendations. And again, once you decide on the sub(s), then you pick a suitable amp to go with them.
You should be able to put together a really good sounding system, way better than stock, for well under $1000. Closer to $500-600 if you shop wisely.
-- Kevin