Speaker sizes
For the front, 6.5"coaxials or components with the appropriate spacer
For the rear, some 5.25" will fit but most people just put 4" speakers in the bracket surrounding the factory speaker(that's what I did).
As for headunits, there are alot of headunits that will look great in the 04 Impreza interior. I've got a JVC LH-2000 MP3 CD player that looks very slick in the dash.
However, if you're looking for XM(not Sirius) capability than you're only choices are Alpine(very nice stuff but pricey and I personally don't care for the designs), Sony(pretty much universally agreed as being crap in terms of car decks) or Pioneer. I've not had any first hand experience with Alpine or Pioneer so I'll let someone else reccomend some models for you.

 

Yeah the LH2000 is an old model. I got it on closeout for 250 from crutchfield.
Here's a pic

I think the LH3100 replaced it.
As for the install, I did everything myself. Getting the dash apart was INSANELY simple. I had the headunit wired and installed in about 30 minutes. The speakers were trickier as I at first couldn't get the door panels off. I still can't figure out how to disconnect the power window controls but I was able to position the door panel in such a way that I get manuever around it even with it still sort of attached. There's a great tutorial here http://users.sisna.com/ignatius/subaru/mods/
Like I said the power window module may be your only hangup. I made my own spacers but if you can buy them from East Coast Scooby if you don't feel like making them yourself. For the rears, if you go 4" just trash the factory speaker but cut the bracket off and use it for your new speakers.
I also installed a Kenwood Woox underneath my passenger seat which was easy also. All in all the 04 Impreza is really easy to install stuff in.