Thanks for all the suggestions, I appreciate it! I do not plan on driving more than a few miles (to the service shop and back, basically) until the transmission is fixed.
Yes, it's an automatic trans - the seller knew that the trans was bad and bought a replacement before selling the car, so I have a 'new' replacement that is in transit (it is RamblinDMC's transmission, 26k miles, complete with GC). The seller had replaced the fluid and filter, but that didn't stop the slipping - my plan is to swap the transmission with the replacement, then rebuild the transmission on the bench and replace all the clutch discs, bearings, and seals. Then swap back in the newly rebuilt original and if all goes well, sell the replacement.
For now I'm going to be working on diagnosing the brakes. I'm a complete noob when it comes to cars, so I have a lot of learning ahead of me on this one!!