You use heat to germinate, not grow, and you use light to grow, not germinate. That's the gist of it but there are endless degrees of overlap between the two modes.

You can supply warmth in any of a hundred ways and a heat mat is just one. You could also site the setup in a warm spot like a utility closet or the like, and move the little things to bright light after they have officially become photosynthesizing plants. There are very few germinating and growing scenarios that require anything to be bought, however heat mats and grow lights are great tools if you need them.

Peat has a few advantages and a few disadvantages, as does every other method. One is they are very good for germinating but please don't leave seedlings to depend solely on the peat pellets for growth. Once you get the second or third set of leaves, move the plant and pellet to some sort of pot with more room. Don't peel off that netting as the roots will ignore it unless they're already growing through it and for some reason (depending on the plant species) you WANT to disturb the roots. This pic shows sweet peppers that are overdue by a few days for transplanting into pots or cups.

The "greenhouse" part means there's a clear plastic cover that holds in heat a bit and that holds in moisture a lot. Unless you have problems, you probably won't need it and at the same time it probably won't hurt. If not using it, watch the peat watering. Pellets can be flood watered if you then let them drip off, and you can get away with not watering until they're NEARLY dry. Completely dry is a no-no. Long term soaking is a no-no. They drain very well and unless they sit in water it's hard to over-water in peat.

As always, since all gardening is local and all techniques are what they are, my suggestion is to wing it, never putting all your eggs in one basket, and split up your germinating into smaller batches that you treat differently.

"Don't peel off that netting as the roots will ignore it "

Many have found that not to be the case:

http://forums2.gardenweb.com/discussions/1397733/peat-pellet-users-you-might-want-to-look-pics