Usually theres loaner gear at the clinics. That's the way to go but...
A few things I look at with bows.
Price point,draw weight and Size. Style
New sport, your riding without reins, your bow gets dropped, run into trees or tossed aside when your horse spooks. The ever popular stepped on. Sometimes cheep is good. Lol You can drop from $125 to $1500 bucks on a bow. I got mine from seven meadows archery but there's other places online.
Style/size there's a bunch of different styles, from mongol to native american flat bow to Scythian, Hungarian and even the 7 ft tall Japanese yumi . Depends on what you are going for,and group your shooting with. Same is true for arrows. Carbon fiber is my preferred arrow ,however I sometimes shoot with the S.C.A. ( society of creative anachronisms) they insist on wood arrows , but fiberglass re curve bows are ok. Almost everyone insists on non compound bows. I like the shorter eastern bows ( mongol or Scythian) so about 48 inches tall max. But that's me.
Draw weight / bow poundage
Id recommend 30 to 35 lbs at whatever your draw length is. That's different than bow weight Bows are usually figured at 28 inches if you draw 30 inches on a 35 lb bow the draw weight is actually heavier. ( see your local archery shop to figure this out but draw length is how far back you pull the arrow at max draw) Its usually not a big deal on lighter bows. Most folks have bows rated at 25 to 35 lbs the amount of arc needed on longer shots changes depending on the power of the bow. 30 to 35 lbs you can shoot all day long and has enough power to hit your target.
The best piece of advice I can give is do what works for you.! The top archers in the sport all have different styles and most will tell you their way is the best, From the way you hold, aim and draw the bow to style of bow you use to breathing. They will insist ,sometimes forcefully ,that their method is the best. IMHO if that were true than the other cultures wouldn't have developed different methods.
The only thing Katie insists on is you and your horse have fun. I really like that about her. If you come to one of her Washington clinics I might see you there. Or perhaps in turkey for the world championships
Hope this was some help.