Astra--starting seeds can be a little difficult. It takes room, good light, and good air circulation. Tomatoes and peppers need to be started about 6 weeks before you set them out.
I start tomatoes and peppers, and have good luck, but I have a southfacing sunroom, and a shelf and light set up that I bring up out of the cellar every spring. I also set up an oscillating fan as soon as the seedlings pop up.
Don't worry a bit about squeezing the bottom of the pot to get those seedlings out--but DON'T grab the stem or leaves, or pull from the top. One method is to turn the pot upside down, with the stem of the plant between your fingers, and smack the bottom of the pot with your other hand. Or, if you are using those flimsy 6 pack pots, just push the bottom of the pot.
I don't like peat pots, either. If you leave the top of the pot above the soil, it acts like a wick to move the water from the root zone to the surface where it evaporates. If I buy a plant in a peat pot, I pull the pot completely off, and crumble it into the soil.
Plants at my greenhouse are not anywhere that expensive--but plants in fancy markets can be--I actually saw grown bean plants, with beans on them, for $15. Silly! A packet of bean seeds is a couple dollars, and if you buy a grown plant, you have no idea about what chemicals have been used on them.
Look for a 'country' store--somewhere out of downtown that does not cater to the 'urban homesteader' crowd. Seedlings are kind of expensive, but shouldn't be anywhere near $10 each. The farmers market may be a good place, but I did pay $3.50 each for pepper plants a couple of weeks ago!
Beans, zucchini and other squash, cukes, basil, lettuce--all those things are easy and quick to grow from seeds. Pole beans need sturdy support--buy 3 eight foot bamboo poles, tie them together at the top (use wire or some kind of string that won't disintegrate in the sun), and make a teepee. Cukes can grow on a trellis, too, saving you some room. Fasten it to a sunny wall.
Lastly, (because I have already written a whole book here!) gardening is one place where you learn as you do. Find your local Extension office--they may have a beginning gardening class, they have horticulturalists available to answer questions and they certainly have guidesheets to help you. (Google "Minnesota Extension, your county name" to find them--we are often hard to find in the phone book.
Oh, wait, one more last thing--finding an experienced gardener to help you is worth a million dollars. Ask questions here, or at your Extension office.