First, note that if you're using indexed shifters that you need to match the number of cogs on the cassette to the shifters.
Cheap wheels are normally not worth the money -- you'll have trouble keeping them true or from failing, especially in a difficult situation like mountain biking.
On freewheels and cassette installation, I'd suggest reading this link from Park Tool.
Freewheels are used on cheaper wheels, and are only really good for <=7 speed systems. They do sell a few 8 speed freewheels, but they were essentially phased out due to axle breakage. To install a freewheel, you simply need to have some grease on the threads of the freewheel and screw on the freewheel to the hub by hand. Riding gently for a few miles will tighten the freewheel all it needs to be. To remove the freewheel, you need a freewheel remover tool (compatible with the freewheel being removed) and a large crescent wrench to turn it (or better yet, a bench vise).
For a freehub system (which uses cassettes), which is used on better 7+ speed wheels (and all 9+ speed wheels), you need the cassette tool (compatible with the cassette you're going to use) and chainwhip and a large crescent wrench to turn the tool for removing the cassette. To install it, you do not need the chainwhip.
Also, if you don't own a chain tool, you'll need one to install the chain (or at least shorten it appropriately).
My recommendation is that you look for a used wheel or a cheap wheel from your local bike shop. The parts you've selected won't work together, since cassettes only go on compatible freehubs whereas the wheel you've selected is designed for freewheels (and you've selected a freewheel). That will be a much better use of 75 dollars.
As for out of the two options you've given (not recommended), if your bike is 7 speed or less, I'd be marginally more inclined to buy the wheel and a freewheel and a small container of grease (multipurpose grease like the stuff they use for cars will work fine). If its 8 speed, and you're really on a budget, you can use an 8 speed freewheel. Otherwise, you're going to have to go with a cassette wheel, and that you have to go to the bike shop or find a wheel with a freehub. But I'd really recommend using a bike shop or spending a bit more money on a wheel, since fixing low quality wheels is not cheap at the shop (which you'd likely have to learn or pay the shop to do with such a cheap wheel), and wheel failure is not fun.