Neither -- you won't have any success with traditional artichoke varieties like Green Globe or most of the Italian ones in our climate -- they can't overwinter outdoors and are too hard to overwinter indoors really without a greenhouse. I have had some success overwintering the roots by digging them fairly late (around Veteran's Day) and overwintering below the frost line in a deep pit lines with straw.

What you need to do is plant Imperial Star or Emerald, the "annual" types that bloom the first year from seed following a vernalization treatment -- start seeds indoors in March, move the little plants outside in April so they get a good dose of chilly weather, then plant, and they'll bear artichokes from around late July into October.

There are a lot of threads on here about this. Do a search for Imperial Star and they should come up.