IMO sounds tight. If you want a good idea of plant spacing requirements then access a square foot gardening plant spacing guide - many available via internet keyword search. This will give you a good idea of what size garden you will need for what you have on your list. Seed packets should also carry spacing information. Follow those references, I find them to be generally accurate.

Do not forget to include human access in the garden. Can get very frustrating having to climb over plants all season while carrying harvested produce, or accidentally stepping on your nice veggies when getting in to harvest. You also need to be able to get in to weed and do other gardening chores.

Going vertical as you mentioned is a very good idea when space is at a premium. Do it wherever possible.

Melons consume a lot of space for what is IMHO a relatively small return, can be hard to justify in small gardens. But if you really love them, then find a way to do it.

Over-plant a garden and you will regret it. This takes discipline until you gain more experience. Planting garden too tight can get very frustrating once the plants size up affecting yield amounts, sizes, and overall quality of produce, and can really affect the enjoyment of your garden and your hobby.

My two cents for what they are worth.

Good Luck.
-Tom

As Tom said, you have some things that take quite a bit of space. Vertical growing will certainly help. I noticed you mentioned 3-4 cherry tomatoes, unless you REALLY love cherry tomatoes you might be able to cut back there. 1 cherry tomato plant can provide enough for several people.

Thank you very much for your input. I will definitely go vertical with as much as possible. I also plan to cut back on the cherry tomatoes and peppers to hopefully leave a little more room to maneuver.

Also make sure you choose a short vined cucumber variety, something like Bushcrop or Spacemaster. I think you will need to skip the peas this season, because they need to be planted early. if your soil is clay based (we have no idea where you are gardening), the ground won't dry out early enough in the spring for you to safely rototill without destroying the soil structure. Whether it is digging, hoeing or rototilling, any kind of working with a soil that is still too wet, is a really, really, REALLY a bad thing.

This is how new gardeners unknowingly create a cement like soil texture. Adding dry soil amendments helps in the long run, but you still cannot incorporate them until the native soil dries sufficiently.