Congrats on the purchase! I just bought a 2011 PPV with 71,000 miles for $7500- I just picked it up yesterday too!
I'm fairly mechanically inclined (cut my teeth on a 300zx) and just looked through my Tahoe. A few pointers:
1. Check your driver side motor mount. If it hasn't been replaced yet, it's probably munched.
2. Check your battery trays for rust.
3. Make sure all of the light/radio holes have been properly and tightly sealed. I found a bunch of water under my passenger side vinyl flooring.
4. With your mileage, check your struts for leaks and look through your suspension.
5. Change all of your fluids unless you have good records. Change the oil, transmission, and brake fluids asap. You can send an oil sample off to Blackstone Labs to check the state of your motor.
Good luck. I'm still building a repair/replacement list for my Tahoe.