First of all, good for you! And what a lucky little boy. Nursing during takeoff & landing can help pop your baby's ears so he doesn't get a headache!
I'm very self conscious about nursing in public too, so I got an Udder Cover. I like it, and it has a stiff neckline so I can see my baby, but it's kind of a pain sometimes. Taking it off & on usually messes up my hair, and it draws more attention to what I'm doing than if I didn't use it. It's a lot easier for M. to get my baby latched on, then cover her with a blanket to help block out noise & lights.
A good nursing top can help you feel more discreet. My favorite is Undercover Mama. You can find them on amazon or overstock.com. They hook right on your bra, so there's less fiddling with straps and fabric with a wiggly, hungry baby on your lap. If you wear one of those as an undershirt, you can probably nurse without a cover and without showing any skin.
I agree with getting a window seat, so you can turn to one side and feel like you have a little more privacy. Whoever is sitting right next to you is going to figure out what you're doing, unless they're deaf & blind, so just do what you need to do to feel comfortable.