I would suggest going to an archery range and renting equipment . Compound , recurve bows, alum arrows and all the rest can add up quickly. Perhaps take lessons, purchase later.
years ago I started shooting and before I knew it had hundreds of dollars of "stuff".
good luck

+1. The shops around here will generally let you shoot new equipment to get a feel. And don't feel the need to buy a high end bow on the first round. There are many ready to shoot bows available for under $500. All you need is a single cam bow with a basic whisker biscuit and 3 pin sight. I also see many on Craig's list, but if you go that route, first stop should be the bow shop for an inspection and tune-up. As far as targets go, a basic bag runs about $40 and is good for hundreds of shots with field points. There are also tons of forum articles on how to make your own, stuffed with old carpet remnants or clothing. I prefer not to use foam blocks as they tend to be difficult to remove the arrows as I shoot a 70# bow. It also helps to move your targets around and guess the yardage (which sight pin to use). That skill comes in handy when shooting from a tree stand during hunting season.

Make sure you not only try compound or recurve but traditional bows as well. I had opportunities to shoot the first two before finding traditional archery. I tell ya there is something just almost "dead" about shooting a compound. I didn't like it one bit. The recurve on the other hand wasn't too bad but just do not feel... "right". Plus any compound or recurve I've ever shot was noticeably heavier than any selfbow I've shot. I don't mean in terms of draw weight but the actual weight of the bow itself. Perhaps that is changed.

Another good side to shoot traditional is that it actually doesn't take an entire month's wages just to get decent starting gear. A decent target shooting bow can made out of a board of red oak that you can get at home depot or lowes. While usable arrows can be made using bamboo garden stakes and gorilla tap fletchings, again both of those can be obtained at either of those aforementioned stores. You could also try to make your bow string but be prepared for a major headache. I've tried making one recently. It was not fun, I ended up overworking it and fell to pieces in my hands.

Anyway I've been shooting traditional for about 2 years now. I'm not that good as I don't shoot that often. But shooting a traditional selfbow with no bells or whistles or aids of any kind, while especially difficult for a beginner (well that's if your used to modern ideas of archery), it can be extremely enjoyable. I plan on getting some stumpin' arrows in the next few months as I'm really eager to get out into the woods this fall and do some roving archery.

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Lastly a few other pointers

1.Make sure you get measured for your draw length before either making or buying a bow. The most common seems to be 28 inches draw length but yours could easily be longer or shorter.

2. Make sure to get or make a forearmguard, stringer, and glove.

3. Get a copy of Byron Fergusson's "Be the Arrow". It cleared up some wrong ideas that I had been basing my shooting on for a long time.

4. Last but not least. Do not buy or make a bow with a draw weight that makes it difficult for you to keep the bow drawn long enough to get your mind centered on the target. What weight that is and how long it will take someone to get mentally centered on the target depends on the individual.