A weekend autocross event is a lot of fun and I recommend you try it. Your first few times will quickly teach you what you don't know about going fast around corners...
I used to auto-x all the time when I was younger. In the early to mid 1970's we ran my buddy's TR4 in Sacramento, and even won a few prizes. I later ran my 2L Ford Pinto in college and consistently beat the Bimmer 2002's, which really pissed them off. Could never beat the "set-up" Opel Manta's with race-prepped engines.
In late 1970's autocross started becoming very competitive. We ran my first 240Z and a friend's Alfa Romeo 2000 Spyder and did OK, but could never beat the "serious" cars . Outside club "fun runs", to be competitive, you pretty much need to have a car specifically set-up for autocross.
However, even though my "street" Z can't compete with cars in her class that are "set-up" for autocross, it's still a blast to do a few runs between the cones at a weekend event.