If it's a cheap bike what you probably want is a 7 speed freewheel. Just be sure to match the number of gears on the rear (right side) shifter to the number of sprockets on the rear freewheel. The Shimano freewheels seem to be the best of the cheap options. It probably came with a 14-28 or perhaps a Megarange 14-34 sprocket sizes. The 14-28 will shift better but the 14-34 has a really easy bailout gear for the hills. If you change from the 14-28 to the 14-34 then you may have chain length issues in your big front ring to big rear sprocket combination, not that you should be using that gear anyway.
To get it off you need the appropriate freewheel tool, either the shimano, the Park FR-1 or the Park FR-7 fits better if it's a falcon freewheel. It's very unlikely to be a 2 or 4 pin suntour given it's age. Otherwise if the freewheel is damaged anyway, if you can remove the 2 pin cover on the end of the freewheel (which many people confuse with the way to remove it) this takes it apart and you can then remove the pawls and clamp it in a vice and turn it off counterclockwise.
Or have the shop remove it for you for a couple of bucks. The new one just threads on and is tightened when you apply pressure to the pedals.
As for where to get one, try a bike shop. Check your yellow pages. Any shop should have one in stock of one brand or another. All 7 speed freewheels are compatible with one another.
tony