You don't have to change a thing to autocross. If you change the car, you change the class you will have to compete in when you autocross, and that can be a steep and slippery slope. Few cars are so autocross ready.
You can change a few things and still be stock legal:
EXHAUST from the cat back - in other words, the tailpipe and muffler. There are plenty of systems around that are popular. I have the enthuza that has a lower pitch than most. A nice exhaust note always add to the smiles per mile.
SHOCKS as long as they mount in the same place as the OEM. KYB AGX's are very popular. They are adjustable and reasonably priced.
Both of these mods are fairly simple. I'm no wrench and I did the exhaust while running a temp of 101! The shocks are a popular item for a techday. There are some tricks that make it easier, but air tools and a couple of extra hands make it go faster.