First find out what you got. Measure the rear drop out spacing. Is it 120mm or 126mm? Assuming it's 126mm and the rear wheel has a freewheel hub and not a Suntour cassette hub, the easiest course of action would be to buy a 6 or 7 speed Shimano or Sunrace HG style freewheel. HG style meaning the cogs have these carvings and contours on them:

Then get a Shimano SIS compatible RD. That would be something like a Shimano RD1050,1055, 6208, 6400....
Then shift levers. If you have a 6 sp freewheel get 6 speed shift levers. 7 sp freewheel 7 speed levers.
Finally get a 6-8sp chain.

Oh yeah- Ultraglide is long out of production. Just forget about it. UG cassettes are expensive and not as good as HG.