Lettuce is a good choice, it's quite easy and quick to grow; I started growing it this year and I'm eating fresh salads almost every day. Choose a mix, or grow a few different varieties so you can get an idea of what grows well and what you like the best.
Treat some of the plants as "cut and come again", i.e. harvest the outer leaves when they're ready, the plants will grow some more; if you do this, you can sow them quite closely. If you like, let some of them grow some until they form heads; in this case make sure you read the seed packet to make sure they're properly spaced.
They'll need some good soil, and some sunlight, and lots of water; try to water from the bottom rather than splashing the leaves. You shouldn't get many weeds in pots, but if you do make sure you remove them since lettuce don't like competition...
Most lettuces dislike excessive sun/heat. Too much sun will make some of them to get dry borders on the leaves, and heat will make them bolt (i.e. go to seed, which makes lettuce bitter and unedible). If the weather gets too hot, make sure you water them and possibly give them some protection from the sun in the hottest hours.
For me, they have been fairly pest free, but they are quite palatable for slugs and snails, so keep an eye out for them if they show signs of being nibbled.
After harvesting, wash it thoroughly, dry it using a spinner if you have one, and store in the fridge in a ziploc bag. This will make the lettuce crisper, since being out in the heat can make it "floppy"; it will stay fresh for several days.