You can get all mental about companion planting if you want, there are plenty of books and websites. Some of it does a little bit of good, but a lot of it is rather tenuous at best IMO.
A strictly pragmatic not-companion-planting-related approach would be something like this:
Plant the corn in a squareish block where it will recieve the least wind (b/c you don't want it to blow over) and somewhere along the N side of the garden if possible (so it doesn't shade shorter things too badly)
Plant the rampantly vining things (most especially your watermelons, but also cantaloupe, zucchini and squash) near the edges of the garden and/or in other places where if (when!) they exceed their planned space they will not be fatally overwhelming something smaller or valuable. Letting them lop over onto lawn is fine; letting them lop over onto space previously occupied by peas or some other early-harvested crop is fine; letting them submerge small-statured pepper plants, not so fine
If your beans are pole beans, plant them somewhere a bit sheltered from the worst storm winds if possible, also where they won't be shading other things too badly if it will be an extensive tall trellis system. (Teepees or a small trellis are not an issue)
If you want to save seeds, plant different pepper varieties as far apart as possible; also if your banana pepper is a hot variety and you don't like surprise-hot green pepper seeds, plant it as far away as possible.
If you are planning on doing a fairly strict rotation of crops in future years, it is good to think that through NOW, so you don't discover that every part of the garden has something from the Solenaceae ('maters, taters, peppers, eggplant) and they are thus unrotatable next year

If you are not planning on losing sleep over rotation until/unless a problem develops, then don't worry about it.
Beyond that, do whatever floats your boat
Good luck, have fun,
Pat