Just bought car few months ago, the vehicle is running so so. Runs good when started, although a little choppy changing gears. Particularly going from second to third. The most troubling issue is that the starting is really rough. Problem started as just a hesitant start, now progressing to almost start failure. The engine hums when started, so I'm not concerned that the trans is troubled. Is this just a matter of clogged plugs or something?

Since this car has an engine that requires valve adjustment, have the valve adjustment checked. Also have the spark plugs checked, & while you are there have the compression tested.
This car also has "Points" & they can cause starting problems when dirty or out of adjustment.