The front are 4inch rounds. They're fairly easy to install. The best way to do it is to pull the door panel loose, but not off. On the bottom of the speaker cover there is a screw, remove that and the whole cover should come off.

 

rears I put 6.5" Alpine Type S speakers. Mounted right in. You need to pull the entire rear deck off, can't just remove the speaker covers. Don't worry, it bends, so don' be afraid to pull that mofo.

 

not sure of the sizes, however you could check out CRUTCHFIELD.com they have an awesome fitment guide, that could help you. And if you happen to purchase any of there products they usually include installation instructions as well as any extra wiring and hardware you may need.

 

Crutchfield says 7th gen cars take 5.25" rear speakers. However I have looked in our 96 and I'm pretty sure I can make 6.5" ones fit. That was the case with my old Camry. It involved a bit of cutting but I got them in and they sounded great.

 

Hey, congrats on the decision to get a new sound system. I had a 600 dollar sound system installed about 2 years back on my 97 DX, and here's some of the lessons i learnt...
- Don't get door speakers installed if you plan on turing up the bass at all. The door itself and the speaker mesh will rattle like crazy unless you put some heavy padding in there.
- Do invest in rear speakers. 6.5 (maybe 6) inch circle speakers are more than enough to get some hardcore sound. Your car probably doesn't already have speakers in the back (as mine didn't either) but your local bestbuy can get them installed for you nice and easy.

As for what system to get, after tons and tons of research...Kenwood Deck...Pioneer speakers.
They work beautifully in tandom with eachother. I'm sure you can find much more expensive systems and speakers out there, but in terms of bang for the buck, these two are top of the line before getting into the luxury quality speakers (which are hardly noticably better). Good luck boss, expect to spend about 500 (CDN) or 400(US) bucks if you want to really be happy with your new system

 

I prefer Pioneer decks myself. I had Boston Acoustics speakers in my old car about 10 years ago and it really sounded excellent. Those are the only speakers I've really had experience with. My Integra just has some cheap aftermarket replacements because the stock ones were blown when I got it.

 

Personally, I'm biased towards Rockford Fosgate as that is what our Mitsubishi has. VERY clean system, and very loud as well with a great EQ. I think the Infinity system in my brother's Dodge is warmer sounding, which may work better in the Corolla as I find the angle of the rear speaker placement puts them level with your ears, which can lead to an obnoxious "ice pick" sound due your ears picking up more treble at that angle. The sub on the R/F is great though... literally feel it in the rear seat! I think the Rockford Fosgate system also has a tighter sound, but that could just be my EQ settings. Bose stuff is overpriced imo, with a lot of it being made in China despite the price tag making you think otherwise. I know JBL makes GREAT monitors for live sound applications, but haven't tried their car audio products. As for Alpine, never tried anything by them, but I'm looking at one of their units for my Suzuki, which has some crappy OEM Clarion unit which is going out.