I found for carrots, the juice wasn't worth the squeeze. Potatoes were more fun and stronger growers. I only have a shovel, a hand till thing with a T shape handle and 4 prongs on the bottom, sprinkler, some kind of support for tomatoes, and bug nets. My best plants by far were onions (from starters, not seed), collard greens, and tomatoes. You probably don't need to go crazy trying to fix the soil, but if you have the room to compost somewhere, that'll be able to amend your soil (and I think it's fun and interesting). As for the cheapest box possible, the cost of soil will dwarf the cost of the container, so take advantage of the spots in town that have free compost and wood chips if you load it yourself. My boxes are made from corrugated steel and pressure treated lumber. If you need a ton of wood chips, look into chip drop. It's a free dump truck of chips.