If you are going to re-use containers from last year, and are going to grow peppers, tomatoes or eggplant, it is a good idea to bleach the pots first, to eliminate any possibility of bacterial, fungal or viral diseases carried over from the previous season. Though not the most fun gardening task, it can be made pretty easy and quick by partially filling a large trash can with water and adding half a bottle of bleach. (be sure to use gloves....I also do this outside). I dip the pots into the dilute bleach, and use a brush to lightly scrub the bottom and sides of the pots. Rather than rinse with clean water, I then just invert them in the sun to allow for the pots to dry. They are then ready to go.
As to what to fill the pots with: this is the one area that I don't "go cheap". I also don't reuse the potting mix year to year for tomatoes, peppers or eggplant, starting with new material each season - again, to minimize possibility of diseases. I use 2.5 cu ft bags of soil-less mix, such as Miracle Gro, mixed with 25 lb bags of composted cow manure - both available at the big home stores like Lowe's or Home Depot. The reason for the soil-less mix is its lightness and porosity. Because it doesn't compact and turn to muck when wet like soil, it makes for happy plants. Of course, if you have access to supplies of nice fluffy compost, you could use that instead of the soil-less mix. At the end of each season, I empty the pots into a pile, with the used mix fine for flowers or herbs or mulching the garden beds the following season.
As far as feeding, I like to grow my tomatoes quite lean and actually don't add anything for a few weeks; after that, I use a slow release, balanced granular food such as Vigoro or Osmocote. If the plants look like they need a boost while in mid-season and growing vigorously, I will use the "blue stuff" fertilizer - Peter's or Miracle Gro soluble plant food. Don't forget - when growing in pots you need to water frequently, so nutrients can leech out of the mix quite quickly.
Once I settle my plants into the growing medium (being sure to plant deep, as tomatoes will root all along any buried parts of the stem; I do this to peppers and eggplant as well), I put a heavy layer of mulch into the container, covering the medium completely to a depth of 2-3 inches. I use fresh grass clippings (we don't treat our lawn with anything). This layer of mulch helps conserve soil moisture, and breaks down to feed the plants as well.
Finally comes the matter of supporting the growing plants. It is difficult to grow indeterminate tomatoes in the middle of a patio or driveway because of the inability to pound a sturdy stake in or near the pot. That's why I grow mine at the driveway edge, with an 8 foot stake pounded into the ground next to the pot into the lawn. If you are growing determinates or dwarfs in pots, then a relatively short stake (4 feet or so) in the pot should work fine - and you can always use the metal tomato cages that you can find in garden centers that are 3-4 feet tall. When using stakes, I use twine to tie the plants to the support.
To remind on watering.....the worst thing you can do to plants grow in containers is to let them dry out for an extended period, especially if there are fruit on the vine. This is a sure way to end up with blossom end rot on the developing fruit. Plants tell you when they need water - if they look really wilted on a hot day, give them a drink! If you use good planting medium, as I described above, you can't really over-water! In the mid-summer, with mature plants, I actually water each morning and each late afternoon, letting the hose run into each pot for 20 seconds or so for a 10 -15 gallon pot - water will run out of the bottom, which is fine.
So there you have it - in three parts, quite a lot of information on growing tomatoes, peppers and eggplant in containers. If you have any additional questions, ask!