I've got a 69 vintage racer Camaro but don't have it running yet.
I vintage race a Lola T-70 Can-Am car and the big events won't allow a newly built Camaro entry to their events.
For entry to a vintage TRANS-AM event the car must have run in the origonal Trans-Am series BEFORE 1973.
Many other groups are not so pickey.
The SCCA San Francisco region allows any car to run if it is old like the first gen Camaro and has a 302 engine.
You can start off with autocross, then run some SCCA Solo I events on race tracks. The Solo I requires an SCCA liscense, which usually means you will have to attend a driving school, (can be in your car.)
There are some other clubs like NASA, here that hold "open track" events and run cars in half hour sessions.
Pick up your local SCCA monthly newsletter and see what events are at your track.
Go out to them and talk to the competetors and see if there is anything you like.
Check my web page for First Gen Camaro suspension info:
David's Motorsports page
First Gen Suspension Page
67 RS 327
69 Camaro Vintage Racer
65 Lola T-70 Can Am Vintage Racer