Just bought an '81 Vette with a rebuilt 350 with 5K miles on it. What weight and type motor oil is reccomended?

I personaly would run amsoil 5w-30 or royal purple 5w-30. Those are a full synthetic and I can tell you from experience they are great. I run Royal Purple in my silverado and Amsoil in my cbr 600rr. Also, from independant studies done on Royal Purple and Amsoil they can go longer between oil changes then most oils. Royal Purple has been tested after driving 22,500 miles and still could be used if you wanted to leave it in the engine. I usually change mine around every 10,000 to 12,000 miles.