It's not necessarily the peat that is the problem, but the pellets are encased in a netting that can inhibit root growth in spite of what the manufacturers say. If you use them to start your plants, cut and carefully peel the netting off when you pot up or transplant to the garden. Don't use 'garden soil' as it will carry bugs and pathogens that can kill your seedlings. Straight peat can compact, dry out and crust up, or hold too much moisture...starting mix has peat with vermiculite and other stuff(perlite?)mixed in. It is also sterile. I use Jiffy starting mix in cell packs, then use potting mix when I pot up to 8oz cups after a few sets of true leaves.
As for peppers, you can find a lot of info perusing the Hot Pepper forum(growing info applies to sweet peppers too). There will be as many different methods as there are posters, and no way is THE way. What works for one may not work for another. Don't forget to read the FAQs at the top of the forum page.
Peppers seeds need warmth to germinate, about 85 degrees is ideal, but they will eventually sprout at temps a bit lower. Keep the medium moist, but not wet. Some varieties will take longer to germinate than others and I've found it's best to keep different varieties in their own cell packs or pots so you can take sprouted ones off of the heat without disturbing the others.
Don't fertilize your seedlings until they have a couple of sets of true leaves, and then do so with a very weak solution.
Also, you don't say where your location is, if you're starting your seeds indoors, what kind of light source you have(lights, bright window?)and that info would help with feedback. Hope this gives you a starting point.

Here is a link that might be useful: hot pepper forum

I like a potting mix such as Ferti-lome Ultimate. Mass sow seeds in a container of it, once they germ and get a couple sets of real leaves, transplant them into 3" nursery trays. Let them sit for about six weeks under lights, feeding them from the bottom with good nuits (Tomato-tone is my fav) and you end up with strong seedlings when it comes time to transplant.

Mike