People have certainly successfully started seedlings on a sunny windowsill, but you'll probably get better results with lights.

You don't need expensive growlights. You can buy an inexpensive fluorescent shop light from a hardware store (or a place like Home Depot or Lowes) and the cheapest bulbs they sell, which will probably be "cool white." For seedlings, the intensity of light matters more than the spectrum. If you want to get fancy, they'll probably sell "sunlight" bulbs as well for a bit more money, but there isn't a lot of research to suggest they're better at the early seedling stage.

Keep the lights close to the seedlings, but not touching, and make sure you'll be able to raise the lights as the seedlings grow. Conveniently, every shop light I've ever seen comes with S-hooks and a chain, to make raising and lowering easy.

Good luck,
Linda

Linda has it succinctly nailed. I bought my 4' fixtures (each holding two bulbs) for under $10 each. I use cheapo cool white bulbs. I use three of these fixtures in parallel (six bulbs) over four flats. It works great. When she says close, she means real close: within 2". It doesn't matter if a couple seedlings come into contact with the bulbs, the lights don't get that hot. But ideally you do not want many of them to be touching.

-J

Well said by Linda dn Uj.
Using a window often leads to leggy, spindly seedlings that generally stretch to follow the most intense light.
Not to mention cold drafts and the dwell time they would be exposed to natural light from a window may be insufficient.

Paul B.

What temps do the seeds need to be at when I plant them in mygrowing medium?

I don't think the temp is all that crucial once your seeds have germinated. As a guess, I'd say you'd be fine anywhere from 55 degrees F on up. I used to set up a timer on my lights as well, which you may find useful (I set it at about 12 hours of light). I also used a fan to make sure soils dried between waterings (to avoid fungus) and to help strengthen stems. Good luck!