Well, here's my anecdotal account: this is my first year growing peppers, and I had two plantings, one in early February, and one in mid-March. I decided to use the heat mat (actually, an old bottom-heated reptile tank) for the March peppers to help them move along, keeping the tank around 80-85 degrees. My heat mat seeds sprouted in 4-6 days, whereas some of the seeds from February are just now starting to sprout. To their credit, most of the seeds I started in February sprouted within two weeks at an ambient temperature of about 70. So, heat mats are only necessary if you're on a timetable, or if you're growing some of the more finicky varieties.
As for lighting, just from my experience seed-starting in general, only the sunniest of windows can produce anything close to the results of a grow light. A simple shop light setup works wonders, and they can be relatively cheap. If, however, you are blessed with a large, south-facing window, you should be okay.
Another important consideration with windows is if they are poorly insulated or drafty, it could potentially stunt your peppers' growth.