Im new at composting, started last fall with leaves, veggie scraps from kitchen and used coffee grounds from starbucks. My compost is going pretty well, got hot, then cold, then warm, cold, and now is hot again. Getting the right combo of carbons and nitrogen is the trick. Also remember to keep it moist, not wet. You should check the FAQ it has all the answers for your questions. Also, I read somewhere else that dairy products are not good for beginners because we not always get the pile really hot and the dairy just sits there and gets funky,smelling and attracting critters. I would not buy anything to start the compost and would save the peat (a practically not-renewable product) for other purposes. Good luck, and enjoy the process.

Here is a link that might be useful: The Lagunites Gardening Experience

This is EXACTLY the right way to start your compost. Its what I did 3 years ago and I've gotten 3 doses of high grade compost since then.
A couple lessons I've learned:
Endevor to keep plastic out of the head end of your compost stream. I find it annoying to pick the plastic out (especially the plastic envelope windows that've been through the shredder) of the garden.

Don't worry about staples, they rust away to nothing in the compost.

I can't see any difference between composting clay coated and non-clay coated paper.

Sod composts better if your turn the pile a couple times.

Lasagna people will give you crap for composting sod ;)

Keep your bin as tight as possible around the base to keep big animals like dogs out. Nothing keeps out racoons, learn to live with that.

If you're doing it right it doesn't smell real bad when you're turning it, even when you dig into something gross like a half a mellon.

If it smells bad it needs more browns, paper, leaves, straw etc.

I don't feel half as annoyed about junk mail when it all goes into the compost.

I still can't compost all my junk mail :(

I wouldn't add the peat, and very little soil, if any. A little bit of soil might help introduce soil organisms, but it doesn't need to break down, and it's heavy, so large amounts won't add value.

However, I'm all for starting your compost with whatever it is that you have on hand. It's great to strive for the ideal carbon-to-nitrogen ratio, and by all means you should aim for it, but in the end, everything will rot, so put it in a pile and get it started!

I can't believe I never thought about how staples would rust away to nothing--iron oxide. Heck, that might even be good for the plants. I've always taken pains to remove all staples. Suddenly, I feel silly! I'm glad I read this thread!

Compost starter is unnecessary, so is the peat and the soil.

I always compost what I have, I don't "buy" things to compost, seems silly to me.