A very cheap way to "road race" would be Autocross. You in a closed course defined by cones against a stopwatch. Usually three heats, sometimes more if you can fit them in in a day.
Great fun, and no chance of scraping paint.
Check out SCCA Solo (another name for Autocross).
Yet another form of motorsports that has been around for ever, but not well known in the US is road rallying. Not quite the Pro-Rallying you hear about on your X-Box 360, Road Rallying is also a timed event, but on open roads and quite legal. Road rallying promotes following a course defined by instructions that a navigator (aka, co-driver) reads off to you from the passenger seat and you, the driver, follow. Interspersed throughout the course are checkpoints where your time is recorded. Arrive too late and you are deducted points. Arrive too late and you also are deducted points. The goal is to drive the "perfect time". Of course, being written driving instructions, if you get lost, you have to get back on course, thus times can be thown off -- part of the fun....
Again, a blast to drive, and little chance of nicking the Goat.
Oh, and to your question of road or drag racing, I actually like both, and have done both. Each very different from the other, but both a blast and quite easy to get into from a $$$ point of view. There are different classes from mild to wild, so your bone stock Goat can compete very very well.
Jim Miller
'06 M6, 18", Phantom Black (haven't raced it yet...)
'02 Saab 9-5 Aero Wagon (probably won't race it -- wife's primary car)
'93 Saab 900 Commemorative #116 of 325, modified (Drag raced, autocrossed, and road rallyed...)
'91 Saab 900 Special Edition
