gosh! where do we start?
there are literally hundreds of realistic possibilities. including electrical, mechanical, and fueling. a systematic approach involving a good grasp of the nuances in the symptoms is essential. and that would involve first-hand observation i'm afraid. an expensive replacement of major parts, many of which are probably not the cause can be effective if not on a budget.
i've gone through a similar experience...after purchasing a non-running car, i eventually got it running, but not running "right" once warmed up. i ended up taking it to a long-time professional. he is in his 80's. the first time in my life i've had to do that, and after installing a rebuilt non-original distributor and a rebuilt carb (both were rebuilt by the gentleman) and finding a vacuum leak (my guess as to the root cause, and something that i didn't have the resources to track down) he had it running better than ever.
i plan on re-installing, some day, the distributor just to see if it was truly part of the problem. and i might do the same with the carb too. ...mostly to satisfy my own curiosity.
