Double DIN are pretty standard fitment, I believe there are really only 2 wiring plug set ups and its not too hard to cut and shut the wires too suit, its a bonus if you can solder and you're not colour blind (ha ha re colour coded wires, oops sorry).
Toyota has the Toyota across the front but, I guess some careful Black Paint or some cute Hello Kitty (tiny) decals would help. Late Corolla CD stuff is Fujitsui which is pretty good factory stuff, around $550 retail for single stack and $900 for 6 stack Corolla Sportivo. My wife has 2004 Corolla and CD is pretty good
and 2nd hand you could be sure hasn'tbeen used too much as they're still current model, not like buying a 10 years old unti and the head packs it 2 weeks late.
JB has some good specails at the moment, but Double Din is a bit rare new and mostly $500-$1000 (I know, I went looking recently and ended up buying Sportivo 6 stack Dble Din so I too have fact 2004 CD for sale! (but might keep for long term spare).
Good hunting