Liquid fuel stoves are still the mainstay on the Appalachian Trail but the availability of canisters along the trail has greatly improved.
A liquid fuel stove is going to be more versatile but it will require more care and set up time. Almost any grocery or hardware store in a town along the trail will have fuel for a liquid fuel stove. A canister stove is going to be easier to use and in most cases lighter. You may occasionally run into sections of the trail where you have difficulty finding the right canister for your stove.
What you choose to cook in is purely preference. Some hikers will have elaborate pot and pan setups. Most will just have a simple pot to boil water or heat soup. You can't be wrong, you just have to decide what works for you.