There is a lot of information on-line regarding container gardening, and your local library will likely also have some books on the subject. You are really asking for more information that we can probably supply here, tho' I'm sure several of us will chime in. Especially suggest you check those resources for information and guidance regarding soil mix.

For early spring, consider peas - snow, sugar and/or garden to climb the fence.   leaf lettuce, mesclun mix, kale and spinach all do well in pots and are attractive. plant more lettuce a bit later in the area that receives partial sun. Also green onion.

Cukes and squash will climb, but would do better on an incline than straight up. might be better to mulch around the pot and let them trail. You will need to keep very, very on top of watering with them. Pole beans probably would need string to twine up, but some one else would have a more informed thought about that - I rarely have grown them, preferring stringless bush fillet beans. Scarlet runners or hyacinth pole beans would be pretty, or some of the newer cultivars with very, very long, thin pods.

Nasturtiums, violas, violets and pansies are all edible and do well in pots. So do garlic chives and society garlic, but you may be too far north for them, especially society garlic.
I'm guessing turnip greens and radishes would do ok in pots.

This past year was the first time I tried tomatoes in pots. The cherry tomatoes did really well. The patio tomatoes (better girl) did not yield that well and the flavor was so-so. Magnesium deficiency can be a problem with container-grown tomatoes. Check the seed catalogs (print or on-line) for varieties of tomatoes that are suitable for pots. Johnny's Selected Seeds gives unusually complete and honest information. Park Seed and Burpee catalogs are prone to hyperbole. (Their seeds are fine, if you already know what you want, but don't trust the blurps.) I haven't tried peppers or egg-plant in pots.

Remember that with most greens, cukes and squash you will need to do succession planting to have a long yield time.

Good luck.