A wiring harness adapter is not neccessary, but it makes everything easier. You'll need to solder the connections or use butt connectors and a crimp tool such as these items. You probably can find them locally for cheaper than if you ordered here.
http://www.partsexpress.com/pe/showd...number=095-250
http://www.partsexpress.com/pe/showd...number=360-630
If you are going to put that stereo in, you may need a bin if you don't already have one in the car. What type of radio do you have in there currently? If you have Radio/CD/Tape player, then you will need to get the bin. If you have a Casette
OR CD player with radio and there's a bin above or below it, you won't need to buy one.
The Gen4 Camry have 6x9s in the rear. You can use MDF and fabricate brackets, or have someone else make them. Another option would be to drill the holes neccessary to install the speakers.