You've just gotten a bit of a tricky first car to own. The 3.7 in the D2 platform is a finnickey engine at times, but it's actually fairly simple.
1. Take the car in to an authorized Audi technician or dealer (try for a technician. Dealers like $$$) and get the car checked out.
2. Make sure to have the transmission filter changed and fluid checked/changed.
3. Make sure to use Castrol Synthetic oil. If it's summer, 5w-40 is recommended. For winter, I'm not sure (I know the 4.2 gets 0w-30).
4. If you have to change the timing belts, you might as well have the valve cover gaskets and cam gaskets changed (they end up leaking onto the manifold over time).
5. Unless you're extremely good at car work and have experience with Audis, don't mess with this car. It is Audi's flagship for a reason.
6. With this car, brakes are everything. If you need new pads, use Hawk HP or HP Plus pads. Stopping faster=lower insurance and blood pressure.
7. Check out www.audipages.com for tips and tricks.
If you have any questions, you can go ahead and message me. I've pretty much rebuilt 1/2 of my car as is.