I grow petunias from seed every year, they're very simple. You can use a regular seed starting mix in pots or the little peat pellets you can get at most stores in the spring. Moisten the seed starting mix or pellets first, then sprinkle the seeds on top. Don't cover them, and only bottom water if needed. Put them under florescent lights or where they'll get direct sun. If you go with the florescent lights, no need to get special plant bulbs or high intensity lights of any sort, a cheap shop light works just fine. Keep them where the temperatures will stay about 60, and you'll have sprouts in no time.
I have Laura Bush Petunias, both regular and pink, old timey or vining petunias, and some hybrids from Twilley Seed company growing right now. The hybrids are the first time I've ever used pelleted seed, but they're coming along just fine.
I've only grown impatiens from seed a few times, but I don't remember them being difficult. I'll check my notes when I get home, if you'd like. My mother has impatiens that reseed themselves every year, and I've gathered a few seeds from hers that I intend to just scatter in part of the garden every spring.