My recommendations to the OP:
There are multiple ways to do it, and many brands that are acceptable. Here are some suggestions:
1. Try to buy all your stuff on Ebay
or another online discount store like here: http://www.onlinecarstereo.com/
You can go back and forth and find the best prices after you select your individual components. A warning about Crutchfield: they do offer "free" wiring harnesses and install kits for headunits when you purchase through them, but their prices are higher to cover those costs--especially for more expensive gear. The more expensive the item, the greater the price difference between Crutchfield and Ebay.
2. Find a local car audio shop and listen to the different speakers on the walls. You might have to travel to San Antonio, b/c they have a lot of good stores there. Avoid Mothers . . . OK for window tint but not much else. Try Custom Sounds here: http://www.customsounds.com/
. I lived in San Antonio for 4 years (did my residency at Wilford Hall). Custom Sounds have some nice shops where you can listen to the different manufacturers of speakers. That's what you want to do . . . hear the different speakers, b/c that's where most of the sound difference comes from. MB Quartz and Focal and Alpine and Image Dynamics, etc. all sound a little different. You can hear the differences by listening to them with a CD of music you like (bring several different CDs with you) driven by the exact same amplifier in the exact same room . . . next to eachother. You'll be tempted to buy something there . . . and they WILL try to sell you stuff, but just go to listen and make a choice on speakers.
3. Remember that matching a speaker to the proper amount of RMS power is more important than what the speaker can handle. In other words, if you take a Focal Utopia series (which can handle alot of RMS power) and drive it with a headunit's MOSFETs, it will sound like crap, even though the speakers are $1000+. Take a $50 speaker with an efficiency that matches the headunit's MOSFETs and it would sound better in this case.
4. In my opinion, drivers (speakers) driven by an external amp with the proper power will always sound better than driven by a headunit's power. Of course, it will cost more (the speakers and the external amp).
5. As far as choices regarding how to set it up . . . whatever you want. You can get a 4-channel amp and run the front 2 channels to the front L&R, bridge the rear two channels to a single sub, and then power the rear door speakers with headunit power. But remember that you will need an amp which is stable at the lower impedance if you bridge (most are . . . some cheap ones arent'). Along that line . . . know your resistances . . . most everything is 4 ohm in car audio land, but you can find 8 ohm subs and 6 ohm speakers. If you power with a headunit (and you will with your stated budget), stick with 4 ohm speakers and DO NOT attempt to power a sub with the headunit . . . only bad things can happen.
Another choice (best IMO with your budget), power all 4 door speakers from the headunit, and power a single 10" sub with a 2 channel (bridged) or even mono sub amp. Remember, with subs, the proper enclosure (and proper air volume for that particular sub) is more important than the brand name of the sub.
Hope this helps