I use corn as a trellis for my pole beans but i also plant bush beans as well. I also plant squash as a companion to these plants because they help keep away the weeds while they grow.
Tomatoes do need to be supported unless you find some varieties that don't need support. I usually start mine indoors in March in large peat pellets. You can buy small and large ones - for squash, pumpkin, zucchini, tomatoes and peppers you will definitely want the large peat pellets and trays. For annuals and herbs, the small peat pellets are fine.
There are some good websites to figure out how to plant your garden. Some things should not be planted next to others. when you do your search, use the key words 'companion planting'. For example, i plant basil and oregano in between my tomato plants. I planted my cilantro next to my bush beans, my beets with my lettuce and carrots and my onions and chives together...etc. There are special things to plant with all the things you listed above so it's a good idea to look.
For your potato plants - buy seed potatoes because they will be guaranteed to not carry disease. Plant them and let them grow. About 1 month after planting (or so) you have to start mounding them so that the growing potatoes don't turn green where they are exposed to light.
For your garden, add compost every spring and after the harvest in the fall. I like to use my own compost but often I have to buy some more. I add about 1 inch on the surface and then work it in, in each season. I do that so that when the snow melts, the nutrients from the fall compost can percolate down into the soil (I don't know if you get snow but even winter rains would do the same thing). In the spring, I just like to add a bit more of a nutrient boost. That way you don't have to use too much fertilizer (unless your soil is very poor - but then adding compost is even more important because not only does it help with nutrient boosting but also helps the soil retain moisture and allows the roots of your veggies to grow easily. If the soil is compacted, the roots have a harder time growing). For your tomatoes on the other hand, they are nutrient pigs and will likely need a monthly feed with special tomato fertilizer. Your tomatoes should get the sunniest spot in your garden, with the best soil.
One note - when you use the peat pellets - you add water to the tray and the pellets expand (make sure they are fully expanded before you seed). You then seed the pellets and cover them with the clear cover (with a little crack to allow some moisture release). keep the in a place where there is no direct sunlight until most of your seedlings have germinated then remove the covers completely. Water them every couple of days because peat by itself doesn't retain water well.
Oh, also, for the squash, zucchini, cucumbers and pumpkins, mound the soil before transplanting the seedlings.
have fun!
