Boy, did you stumble into a knowledgeable bunch!
I, on the other hand, have just messed with bows, archery, and hunting.
After the accident, I had to give it up, the left arm socket couldn't take the pressure.
BUT, even if you don't get an authentic recreation of a longbow, magyar bow, or native american design, just messing around with simple recurve bows, or the robo-cop compound types, is vastly entertaining. It can be a very low investment, minimal equipment, and undemanding hobby/sport. It is very nice if you have pals who are also interested, and as mentioned by the smart people, most clubs have folks who LOVE to help newbies....
But even without such...you and your fiance can get a couple of light bows, a few books, or website instructions, and share a really pleasant afternoon, developing skills. Bow fishing is more demanding that one might think; bow hunting requires the patience of Job, but both are marvelous.
However, even popping a ballon that is on a target 30 yards away is tremendously satisfying.
By the way, start with the target close, reinforce the effort with success, then move back (Or move the target further away). You don't need heavy poundage bows to start...REINFORCE the satisfaction, then work on the skills--especially true if you have your lady there and she is somewhat self-conscious about it, but true of everyone, really.)
Second to last, be careful not to get immediately sucked into the hypervelocity group. These guys shoot titanium slivers 1,000 kph, with such speed that the laws of gravity almost don't pertain.
And finally, when Pan Tau gave his excellent post, and the great links...please note: They were on HORSES...equines.... NOT MUSTANGS, by Ford.
Be safe.