Your question is so general it will be hard to answer. If you want to race at a track (i.e. road race) first you will need to join SCCA. You will then need to attend driver classes and then log time on the track (non-racing practice). You can complete this in a three day weekend at the right school. Next you need a car built in accordance with the rules. However, you can lease one for each race you wish to participate.

Purchase a copy of GCR (General Competition Rules) and it will describe all of the racing classes and driver requirements as well as equipment. Go to a race and pick the class that you like.

I don't know about solo or autocross.

Good luck