Tomatoes should be firm with a rich unblemished colour; avoid those with soft spots since it means they are too ripe. They will keep in the refrigerator for 4-6 days, although this will depend on how ripe they were when bought. If refrigerated, let them come to room temperature before eating.
Tomatoes are eaten raw and cooked. For the latter the skins can be removed by immersing the tomatoes in boiling water for about 45 seconds; if the skin isn't already coming away from the flesh when they are removed from the water, a quick slash with a knife should release it.
Fresh raw tomatoes are the archetypal salad ingredient, by themselves, as part of a more elaborate mixed salad or with one or two other ingredients like mozzarella, avocado, red onion and basil. For cooking, plum is the variety usually recommended, and is the preferred option for stews, casseroles and especially pasta sauces. Tomato based sauces can be plain (with only herbs and maybe garlic added) or fancy, when other ingredients like onion, white wine, ricotta, peas, bacon, mushrooms or aubergine are mixed in.
Roasting is another good way with tomatoes: halve, sprinkle with olive oil and garlic, and cook in a low oven for about 1 ½ hours to bring out their inherent sweetness. Prepared like this, they can be used as a pasta sauce, to flavour couscous or risotto, and as a starter with goat's cheese.
Tomatoes are also canned, whole or chopped, made into juice or puree/paste, strained and bottled as passata, or dried, particularly sun-dried, to concentrate their flavour. The most popular processed form of tomato is probably ketchup, a condiment that has many culinary uses.