I would say it would depend on a couple of things.
Do you have other transportation for the kids?
An 8 would come with car payments and full coverage insurance.
A 1st gen would be paid for, so choose your own insurance coverage.
8s do okay at autocross.
1st gens can do great at autocross with some changes (which are cheap by comparison with aftermarket parts for an 8).
Your level of mechanical abilities.
As long as you have another car for when you have to haul the kids, I'd say grab a cheap 1st gen for about 2 grand. Put another 2 grand into it for suspension, exhaust, tires, tuneup. Now you are fully paid for (for under your 1st year's 5 grand budget), and a very fun car that will kick butt at autocrosses. Cheap to maintain, and very dependable when properly cared for.
I have an Audi Allroad for hauling the family around, a 328i for winter driving, and my 7 for daily driving during the non-snow seasons. Race on the weekends. Everybody is happy.