You can show up to any events you'd like. If you make half of the available events, you'll be able to get annual tech the following year and are also eligible for a trophy in your class.
The first event is a "school"/test 'n tune and is highly recommended for newbs.
There is a class system based on your mods or lack there of. Google "2010 SCCA SOLO Rules" for the PDF of the rules including classing.
Direct Link:
http://www.scca.com/documents/Solo_R...solo_rules.pdf
Feel free to ask us for our opinions on your class based on mods too.