Lots of good suggestions already, +1 on the Centurions.
More suggestions:
Note some of the old timers here on this forum, I've never seen so many beautiful restored bikes and have gained tips and some cases some serious envy. Most of them are real artisans and may have one time even managed a bike shop. Hang on the Mechanics forum to get an idea what problems you may encounter and how to fix them. Check the Vendor area for good sources on parts and who to stay away from.
If possible, examine the bike well before purchasing, look for dents, cracks, and amount of rust if any on the bike. Some folks don't seem to mind rust but I do, especially when it starts to perforate your tubes. I have a Mercian I'm saving for a possible restoration hat has a rust perforated fork steerer tube. Riding that and having it snap would not bode well.
Besides the make model and components check the wear on the existing items, if overly worn you may have an expensive rebuild on your hands but more importantly, safety issues. If the owner allows, ride the bike to see if the chain skips on certain gears, how it steers, note any odd noises, and check your brakes to see if they work. Are the wheels pretty centered in the dropouts and are the wheels fairly true (not spinning in an eliptical pattern - bent axle)? If possible, note the area closest to the largest cog in the rear and look closely at the spokes where they meet the hub. If the chain has fallen off into this area the spokes will be bent and will eventually break.
If you buy online, sight unseen based on a few pictures, caveat emptor..... I for one will no longer buy items sight unseen unless knowing the source personally.