you will curse the day you plant mint in your garden! plant in containers, but not in the ground, unless in a VERY out of the garden spot, where you expect it to be the only plant-forever. i know it is hard for the new or uninitiated to mint gardener to believe you can have too much, but it will choke out your other plants. i have been there and done that and boy was i sorry! as for your other questions, i would INTERplant your companion crops, rather than having seperate rows. do a search on google for interplanting companion crops or some such and i am sure you will find some layouts or more specific info. good luck~

not even nasturtiums will survive very long in a dixie cup...

but keeping mints pot bound is needed, unless you want to plant it in a crner of your lawn, and let it grow through- and in your climate, you could grow one of the prostrate (corsican) mints, and treat it just like normal lawnage (only it smells better when its mown)

actually, keeping the bee balm confined isn't a bad idea either...that's another one that can be a bit too pushy for its own good.

what containers? a 5-gallon bucket with the bottom 1/3 full of packing peanuts is ideal, and if you're really slick, you can bury it half-way or more in the dirt, and/or paint it to look less like a 5-gallon bucket.

I would put the tomatoes at the back of the bed, interplanted with garlic and basil (tomato garlic, tomato, basil, tomato, garlic, etc and then plant the marigolds and nasturtiums at their feet, I know nothing at all about the borage, so I would plant it based on height...

and I'd keep a pot of mint at one end, and a pot of bergamot (bee balm) at the other.

i pulled my lemon balm and mint pots from the ground in order to divide, and b/c they were overflowing the sides. i couldn''t even get the lemon balm out of the pot. instead, i had to peel the pot away from the lemon balm. so, a sprig went into another pot and the rest into compost tea. after that fight, i just left the mint pot standing ON the ground by my strawberries!

I have spearmint planted in an 8" clay pot, which is buried in my garden bed and it is doing great. I started it from seed over a year and a half ago and it survived my zone 6 winter. One or two runners escaped over the edge but were easily vanquished. Just make sure that the lip of the pot serves as a border keeping the mint inside.

Also, the unglazed clay works great because it is porous, letting moisture pass through the pot and into the soil more easily.

Mints aren't that scary. They are a real welcom presence in the garden. They do spread aggressively so if anything less "robust" is next to it .... it is best to pot it up.... however if you have the space I see no problem in letting it run. It is fairly easy (shallow roots) to pull up if you want some gone. No a dixie cup will not work as a planter. Mints can get pretty big and even a robust mint would suffer in such a spot.
If your idea is to plant mint interspersed with veggies but you don't want to use pots I suggest just not planting the mint. It will not behave in small spots in between veggies. Better to put another "companion" like chives? or a smaller less aggressive mint like pennyroyal.

I have Orange Mint and also Chocolate Mint in 1 gallon pots all around my garden and they seem to be doing well... so far so good! LOL :-)