I wouldn't bother corn in a container. The others should work. I am not sure about HoneyBunch Toms. For tomatoes you should get determinate types. They don't get as lanky.
1. Go shopping at a plant nursery. You will need plastic cells, 4" to 6" pots, 2+ gallon pots, fine potting soil for starting the seeds, regular potting soil, fine sand to prevent damp off (google Martha Stewart damping off), lights (most windows don't provide enough). I would get a seed starting kit with a heated bottom so the seeds sprout sooner and with a better %age of sprouts. Don't forget fertilizer. Get something for the zucchini to grow up on, a small trellis maybe. Twisty ties to keep it growing up the trellis.
Now how much did you spend? Probably more than you would have spent on the veggies, BUT you will have your own varieties and you will know what poisons (or not!!!) the food has come into contact with.
2. Set up your space preferably near a sunny window. Fill the cells with the fine soil and plant your seeds according to the instructions on the pack. Most seeds can go just under the soil in cells. You don't need to turn on the fluorescent lights until the seeds begin to sprout.
3. Damp off is a biggy if you are not in a well ventilated greenhouse. Damp off occurs when there is a lot of moisture (but seeds can't sprout without a lot of moisture!) and not good ventilation. It is a fungus that attacks the stems of young seedlings. The seedlings topple over and look thin just a few millimeters above the soil line. All your work, time and materials will be wasted if you don't prevent damp off. Sprinkle a layer of sand over the soil and it will help keep the top layer too dry for the fungus to develop.
3. When the roots have pretty much filled the cells transplant the seedlings into the 4" or 6" pots. Keep them in the sunny window with your fluorescent lights. You can now start fertilizing. Fertilizing too soon can also encourage damp off.
4. When the roots have pretty much filled the smaller pots you can move the plants up to the final size. Anything less than 2 gallon pots will likely not give them enough root space and may get too hot in the summer heat. Cilantro is probably the exception to this size issue.
I think that is pretty much it. Be sure to harvest some of the zucchini flowers for the best quesadillas ever (quesadillas de flor de calabaza)!
