What is the smallest gearing I can run on my new frame?
This varies between manufacturers but as a rule of thumb if the brake mounts are on the chainstays, 36/13 is usually the smallest you can run. There are a few manufacturers that make a frame with chain stay mounts that will take a 25/9 gearing but not many. If the frame has the mounts on the seatstays then you can run gearing as small as you want.