Probably 98% of people in America have only eaten artichokes prepared one way – steamed or boiled and then served with mayonnaise or melted butter.
They don't know what they're missing.
Sure, those big old heads are impressive looking (growers call them "hubcaps"). But they're really expensive and they're really cumbersome if you're using them in a dish. You're far better off choosing medium or baby 'chokes. These are different from the big guys only in size, not in maturity or flavor.
They even come from the same plants. A typical artichoke plant will produce only one or two giants, a half-dozen or so mediums and even more "babies." So the big 'chokes are not only the most commonly used, they're also the scarcest, and that adds up to a high price. You can usually find the smaller 'chokes at a fraction of the cost (around 75 cents apiece for mediums, as opposed to three bucks or more for the largest).
So what do you do with these little artichokes? They're great simply glazed as a side dish: Quarter them, put them in a skillet with just enough water to cover the bottom and a good glug of olive oil; cook covered at medium until they're tender, then remove the lid and increase to high until the liquid evaporates to form a syrup; season as you wish (garlic certainly, other herbs as seem right).
You can use this basic technique to start all sorts of dishes — sauces for pasta, first step in risottos, even vegetable stews. The combination of artichokes and potatoes is also pretty terrific, particularly when you bind them with cream and bacon.
One other thing to do with artichokes is to serve them raw. I know it sounds weird, and only a couple of years ago it was almost unheard of. But they're good if you shave them very, very thin (1/16 inch is noticeably better than 1/8) and season them very aggressively with lemon juice and olive oil. They've got a great crunch and a subtly sweet flavor.
How to choose: Pick the freshest artichokes by squeezing the "leaves" (actually, they're bracts, like the "flowers" on bougainvillea). Really fresh artichokes will squeak when squeezed. Choose the artichokes that are heaviest for their size. Don't worry too much about blackening at the stem – that's something that happens very quickly with artichokes – but don't buy artichokes where the stem has started to soften.
How to store: Keep artichokes in the crisper drawer of the refrigerator.