Check out some local sources for a used bike: bike shops, noticeboards, papers, clubs. You want to see before you buy.
Look for a mid-high range bike in steel ,chromoly or a branded steel from Reynolds, Columbus, Tange. Butted tubing if possible. Steel is more reliable as a used bike, than Al or carbon fibre. Titanium is usually too expensive.
If you want fenders or a luggage rack, make sure the frame has sufficient threaded eyelets.
Avoid bikes with crash damage, totally worn out components, or a bike that was crappy when it was new.
A road bike should be fine, but you could also ride a sport-touring or even touring bike.
Fit, fit , fit. In length (bars to saddle) as well as standover clearance.