Chives, oregano, basil, and mint should all thrive under a novice gardener's care. Mint is really difficult to sprout at home, so it's best to buy transplants. Mint spreads quickly so if you don't want it to take over your yard, keep it in a pot.
No time like the present. Look for heavily discounted perennial herbs at your local garden center. They'll likely look pretty rough, but that's fine, so long as the roots are good. Thyme and sage are versatile perennial herbs you could try. Keep them in their pot and let them go dormant. If you tuck them in with your pots they should do fine and will come back next spring good as new. You can put them in the ground or pot them up at that time.
The best use for herbs, that I can remember from childhood, is that they give sauces an extra "layer" of flavor. I think they would grow well in a planter that you put them right outside a kitchen window.
We don't have an herb garden, but we grow a few herbs in pots in our home. We grow thyme, parsley, oregano, and basil because they're easy to grow inside.
There are several herbs that are easy to grow. I like growing lavender because it's so calming. I also grow my own peppermint and add it to my hot tea at night.
A lot of herbs are easy to grow, so pick out a few herbs you think you'll use and start a small garden with those. Basil, chamomile, and rosemary are easy to grow, for instance. You can always expand your garden later on after you get it going.