Most herbs are easy to grow indoors, or so I’ve been told. I’ve successfully raised roma tomatoes indoors until they reached about 2ft, then moved outside (which, barring that option, they’d probably be fine in a bigger pot). You might want to consider buying lights to grow them under, as the light filtered in the window isn’t as strong as what they would otherwise get outdoors.
You should be able to get some “heirloom” labeled seeds even at your local garden stores. Not sure what you have for that in NYC, but even many mom-and-pop owned hardware stores will have easy-to-grow starter seeds. If there is a garden center or nursery nearby, that’s your best bet.
If you’re going to order seeds online, do it from a reputable dealer, like Burpee Seeds, Jung Seeds, Vermont Bean Seed Company, etc.