Sounds great!
It is good to start your Tomatoe seeds in February. You can sow them in flats and cut the plants (and their root balls) out after the cotyledons have finished (and the main leaves have devloped) and then pot them up to larger (4") pots. Once the root ball fills these pots (around April) you can Pot them up into your growing pots and fertilize them weekly with liquid Fish Fertilizer. Be sure to give them a shot of Kelp meal when potting them up. Once the danger of frost has disappeared you can move the pots outside. You should place a six foot stake in the pots and use old nylons to tie the tomatoes to the stake. They will grow great!
Some nice Heirloom Tomatoes are: Zebra Tomatoes (will give you lovely tomatoes through November), Black Tomatoes and Current Tomatoes (you can do these from hanging baskets and they don't need a stake, very sweet).
I've done buttercup squash in pots and that works well. I've never tried cukes but, you should give it a shot. Carrots you would want to do in a rectangular pot such that you can maximize the rows and space that the carrots have to grow. NOTE: Carrots do not like being transplanted so, just put the seeds directly into the pot. Sow them into the soil in early spring (April or May). Basically whenever the danger of Frost is gone.
I have found that it is easiest to just purchase herbs from your local nursery as I have limited success in starting them from seed. The success that I have had came about then I planted individual seeds in 4" pots inside near a window.
But I'd agree with that statement in general; know the plant and it's needs and you can find the right container. I've seen plans to grow potatoes in garbage cans; hows that for container gardening?!