Dodo101 if you go the conversion route
there are tons of cool old road frames out there.
Look for a frame that 1) fits, 2) has horizontal dropouts
and 3) has decent tubing (labels saying Reynolds, Columbus,
Ishiwata, etc.). Steer clear of French bikes unless you want
to hassle with idiosyncratic French thread/size standards.

Japanese bikes from the 80s can be a good value. Miyata
and Panasonic can be found and had for not much money.
Bridgestone less so but still can be found. Vintage old bikes
can sometimes be scooped up for a song. A fellow on the C&V
forum found a fully-chrome Schwinn Paramount with a Campagnolo
drivetrain for $150. An unlikely find, but it is incentive to look.

As others have said the buy-a-starter-fixed-gear route is much
less hassle but you will have something cool and comfortable for
long rides if you take the trouble to find a nice old road frame and convert.