When you first start you will need to make the decision on which of the many archery bows you would like to shoot. There are compounds, recurves, takedown bows, longbows, etc. out there so it is best that you do a bit of research on them before you commit buying your bow of choice. They all have their own unique set of attributes that are made to fit archers of all varieties. Once you figure out what type of shooting you want to do, then you need to figure out how much you are willing to spend. This will help you narrow down your focus and hone in on a decision.
You now need to get yourself something to shoot. The most popular arrows that you will find out there are wood, aluminum and carbon. I have personally transitioned from using the wood arrows in my childhood, to aluminum in my teens, and now the only thing that I use is carbon. Everything matters when you are shooting your archery bow, so you need to make sure that the arrows are consistent. Carbon are extremely consistent, but they will be the most expensive. Aluminum is a good starter arrow because they are relatively inexpensive, and are more consistent than wood. I would suggest staying away from wood arrows until you have developed an eye for purchasing arrows because it is much harder to find a quality wood version.
I would also suggest that you get an archery arm glove or an archery bow release–depending on the type of bow that you purchased. When I began shooting, I mainly liked to use recurve bows. When you start to move up in weight, your fingers get sore after 40-50 shots due to finger pinch — unless you are using a glove.
If you are anything like me, then you will probably also want to get an archery target so that you do not have to drive to your local archery range every time that you want to shoot. I purchased a Bulldog archery target as they offer a lifetime guarantee. This means that I can shoot off a couple of dozen arrows when I feel that I need a little bit extra practice. Again, the archery target is not a necessity like the arrows, and the archery bows are, but having one never hurts so that you can get as much practice as possible out of it.