I have a 1964 Carlton Catalina that I'd like to get in riding condition. I'm not a bicycle expert, so please forgive my lack of correct terminology. The main issue is it was converted to a single speed and all shifting assembly pieces were removed. (It currently rides, albeit a little hard. There's a bit of a stutter in each pedal rotation.) If I were to start over, purchase new gears, pedals, chain, derailleur, etc., where would I start? What are some recommended brands and systems?

The frame is in good condition, the seat is in excellent condition, brakes are OK (need new pads) and I will probably need to retape the handle bars.

Thanks for any guidance and help.