You need make a couple decisions before you can choose what you want. Like what to do want to with the aux jack? do you want to be able to Control the iPod from the HU or just use the ipod to select songs? And most importantly BUDGET.
If you just want to be able to use the iPod to select songs, you can easily just get a new stock radio like lampoon said.
If you want to be able to control the iPod from the HU then you need to go aftermarket, which then opens up even more questions. Do you want to be able to watch dvds? do you want bluetooth? is navigation something you'd like? What about USB or SD capability?
You can get even more advanced and go with something that has time delay correction, multi eq, 7 band graphic eq and 5 band parametric eq and crossover.
Thats just headunits.
You want more power so now you need to look at amps. First we'll take a side note and discuss subs. I recommend a subwoofer for all audio installations. simply because it takes the bass out of the speakers. it will keep you from turning up the bass if you didnt have one to try and add some thump.
Next decision would be how much trunk space you can lose. If you can lose a lot, then i would go with a single 12" in a nice 2ft3 ported box. If not then maybe a single 10 or 12 in a 1ft3 sealed box. Theres also a box made for a single 10 that fits between the back of the trunk and the wheel well. That would be a good option assuming you want all of your trunk space.
Another thing to think about is power. How much power do you want. You 'd probably be good with around 500Wrms. Something like a JL W3 would be a excellent choice for you. Great clean sound and decent power.
Now for amps. Now come even more choices. With a setup like you'd have with 4 speakers and possibly a subwoofer. you can go many different routes, which all depend on the power demands. You can go with something simple like the Alpine power pack which you attach between the HU and speakers and it puts out 45Wx4. It will be a great improvement over just using the HU. If you want that it doesnt power a sub so if you wanted a sub then you're looking at also getting a mono amp. my recommendation would be something like the HIfonics HFi1000D. That will have more than enough power to power a sub.
If you want more power than the power pack, now you need to step up to a 4 channel amp. The difference is you get more power, but now you have a bigger separate amp that you have to mount somewhere. The plus side, more power. My suggestion for that would be a HIfonics HFi100.4. 100Wx4 will be a great amp to power speakers. However then you would need a mono amp again assuming you get a sub.
Another option, this you would only choose if you get a sub, is a 5 channel amp. It will have a channel for each speaker plus one for a sub. The plus side to this is that it takes up less space as you only have one amp instead of 2. My recommendation for this would be a Hifonics ZXi60.4 + 1K. 60Wx4 + 1000W. Only downside to this is you get less power for your speakers.
Depending on your HU chioce there will be 2 ways of connecting to the amp. With the power pack it just connects to the speaker wires between the HU and speakers. But if you have the stock HU and an amp, you will have to go out and buy a line out converter. If its an aftermarket HU then you'll just use RCAs from the HU to the amp. One thing i cant comment on is what you would do with a stock HU and 5 channel amp, or stock HU, 4 channel amp and mono amp.
As for speakers you need to decide, component or coaxial. Component systems have a separate midrange driver and tweeter where as coaxial dont. I prefer component some prefer coaxial. Either way you'll want a 6.5" up front and you can go 6x9, 5.25 or even 6.5 in the back. For companies i would recommend Cadence or JL audio. They've got great stuff that sounds amazing.
Thats pretty much the basics. You need to make some decisions before you go out and buy stuff.