About 1 1/2 to 2 inches is normal clearance. I rode a bike for many years with about 1/2 inch of clearance. The only problem was mounting and dismounting on hills, where the 1/2 inch of clearance became 0 inches of clearance and I had to be careful. You should definitely not buy a bike with no clearance, because even dismounting and landing on a bent knee would be a problem. Mounting and dismounting on hills would be dangerous.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72