It is just as easy to own a rifle, shotgun, or handgun in Vermont. There are no state licensing requirements for concealed or open carry of a sidearm, and there's no registry of any type of firearms (beyond Federal laws for things like machine guns.) Purchasing a gun does require a Federal background check. However, assuming that you don't have criminal or mental illness history, it usually only takes a few minutes to get approval.
It is completely legal to build your own firearms, either long gun or handgun. There is a Vermont state law requiring that if you build one from complete scratch (or from a pile of collected parts) that you must have a licensed gun dealer imprint a serial number on the gun. There's a bit of a Catch 22 however: I have been told by the largest dealership in the state that no gun dealer in the state has the proper equipment to imprint a serial number. It's also illegal to cross state lines with a gun that does not have a serial number, so you can't legally take it out of state to try to comply with Vermont state law.
You can buy pre-serialized parts* and build your own. Buying those parts requires the same Federal background check as purchasing a whole gun. *(Only certain parts are required to have a serial number.)
As far as which one? Most people find learning to aim and hit a target easier with a rifle when they're just starting off.