Virtually anything you might like to grow can be done in window boxes, Josh. It just takes special attention and techniques is all.
Any container garden suffers from a dual problem. By their very nature, they dry out much more quickly than planting in the ground. So you have to water more often. This, in turn, means that nutrients leech out quickly. So you have to fertilize more often.
The smaller the volume of the container, the faster that all happens.
Within that framework, however, what I would do is get the deepest window boxes you can manage. You want at least six inches of planting depth, and more is better. Often this means you have to build some sort of support structure, because the box is too large to merely sit on the window sill.
Get a good quality planting soil to fill the boxes. This is the one time I'd consider a mix that includes fertilizer. In addition, pick up a good 10-10-10 fertilizer, and apply it about every two weeks, using a 25% solution. That is, if the instructions say to mix 4 ounzes in a quart of water, just use 1 ounce.
The only problems you may encounter with window boxes are supporting taller plants. It's hard to stake a tomato, for instance, because there isn't enough depth to hold the stake in place. But you can often devise other supports, such as string trellises and the like. Plus most vining plants (including tomatoes) will happily overflow the box and grow downwards, if you have that sort of room.
If you have specific veggies you'd like to grow, let us know, and we'll try and provide specifics for growing them in window boxes.
I don't know about "best," Josh. But it's certainly not a bad idea to have a few pots of fresh herbs on the windowsill.
One note of caution, so you don't get frustrated. Many herbs are perenials, and don't really start producing until the second year. That is, if you plant thyme, for instance, you wait impatiently for it to put out enough foliage so you can harvest it. And it doesn't happen. And doesn't happen. Then, the second year, you turn around and there's this beautiful mound of thyme.
Other than that, I can't think of a single herb which can't be grown in boxes and pots.