Probably the reason I started out growing herbs is because they're easy and they suffer neglect like a lovelorn middle school boy. Plus, they're just happy little plants that add delicate cheer and are mostly bug/disease resistant.
Select a sunny spot in the garden (mints can do part sun), amend the soil and get some little starts in. Of course you can grow from seed too if you're one of those patient people. You will want to keep any mints in a separate container-it does spread like crazy. Lemon balm can become a nuisance as well. Keep it from flowering and therefore seeding by snipping off the flowers. Here's what I like to grow for medicinal and tasty teas:
German Chamomile: Smells like teen spirit. Okay, no, it actually smells a little like apple and you can mix chamomile with just about anything. Make sure you get the German kind and not the wild chamomile that smells like an old dog. Chamomile is a great calming tea and it settles the stomach. Drink it first before you pop that Gas X.
Lavender: Lavender is good with chamomile and mint and a little bit of sugar. It's more versatile than people think and it looks and smells great as a dessert topper as well. We're talking about the flowers here, not the leaves.
Peppermint: Peppermint is probably the best for tea, but there a gazillion mints that just smell so yummy-chocolate mint, spearmint, etc. Get the ones you like but grow them in a container.
Lemon Verbena and Lemon Balm: Both are lemony-the verbena I think is a prettier plant and easier to control. Or do both. Great with mints.
Echinacea: Not the tastiest plant but it's so darn pretty and usually easy to grow. Make a tea from the leaves or the whole darn stem and flower when you feel a tickle in your throat.
Bergamot (Monarda Didyma): Pretty flowers that attract bees-you can toss the flowers or leaves in a salad or a make a tea with them. Make sure the leaves are young and tender-
Stevia: I haven't actually grown stevia myself since I like to sweeten things with honey. It tastes pretty good, (it ain't sugar) and if you're looking to cut down on your sugar I'd recommend this plant over those nasty sugar substitutes that taste like something that should be poured into your radiator.
These are just some suggestions, there are lots of herbs you can grow for tea. Make the most of your money and get into the habit of snipping them and drying them. If you really want to hippie out, buy some little teabags, make your own dried tea blends and give them to your friends...