As (hell I hate quoting you) I-AM-TEH-FASTEST-11 said, you only need a licence to hunt with a bow...from memory, your covered at a club.
Gekigengar; the actual action of the compound bow and recurve bow is similar...energy is stored in both the string as well as the bow itself but...maybe take a look
here...kinda helpful.
Ive only ever used a Compound Bow once. It was made from composite materials and was perfectly balanced...weighed vitually nothing compared to the ol' recurves...It also featured the use of a stabilzer arm...pretty much countered the bows center of gravity when you had the string pulled back.
I was always curious to know why they had the cams on each end until the lady who let me use her bow, hung it from the string on a set of scales and pulled down...she was pulling at about 60lbs...before the cams rolled over and this became close to 12lbs...virtually nothing...by this stage, your arm would be in the firing position and would make resighting so much more simple and relives the strain on your fingers and arm. When you let go, the energy stored in the cams give the arrow that extra 'kick'...although the arrows we used were more like needles...
From memory, the Junior ones start at around $100 or so...simple fibreglass construction, this carries though to the midrange....expect to pay what 400-600 for one of these. Better quality...lighter...stronger..the advantage list goes on. From there, your getting into hunting and competition bows and they are anywhere from $1000 to $3000.