You should do neither. Buy a used running bike that you can ride and just make upgrades to it as you ride it. I often tell newbies here (but I doubt they listen) there is literally no reason to take a complete bike apart to have a project bike other than cosmetics (eg painting the frame), and cosmetics you do last.
If you really and truly want to build a bike from the frame up - go buy a chopper rolling chassis kit from a reputable company and start there. It will probably take you about 1-2 years of nights and weekends and about $10k all in, and that's the easy route where almost all the parts are supplied to you, nothing is rusty or bent or stripped, and there is a huge knowledge base. Can you do it for cheaper? Sure, slightly, but you really only trade money for knowledge and experience and if you don't have any knowledge or experience you have nothing to trade with.
the truth is the majority of the work of any project bike is research, not spinning wrenches. In order to make something better you must first understand how it works, what others have done in the past to make it better, what are the trade offs, etc....any dipshit can just change parts, but the really great bikes are built with time and patience and intelligence going into every modification.
So yeah, if you want to do this right attend a vintage race and look and see what bikes are most common in the pits. Talk to the racer and see what he/she likes about racing that bike. Then pick the make and model you liked best and search for one in your hometown. Not every bike can be a cafe racer, you need one that has a knowledge base from being raced and aftermarket performance parts support. Don't be one of those guys who thinks any bike can be a racer, because while it maybe marginally technically true for someone with a full shop and decades of fabrication experience, it is not true for you.