Let's start with the bow. Traditional bows fall into two general categories, longbows and recurves, although there are many sub types of both we will keep it simple for this discussion with just these two types. When you are more experienced you can explore short bows, flat bows, Mongolian bows, Japanese bows and there are other types, too many to mention here. At one time there was a difference in arrow speed between the two types of bows but with today's modern materials that difference is gone. What is important when choosing a traditional bow is choosing the one that has a grip that is most comfortable in your hand. The grip is your only contact with the bow and affects how well you shoot.
You need something to shoot out of the bow and that would be an arrow. Arrows come in two basic materials, carbon and wood. Carbon arrows are more expensive but very durable. Wood arrows are cheaper and more traditional. It does not matter which type you choose as long as it is matched to the bow. If an arrow is not matched to the bow then it will never fly properly.
One of the big mistakes made by newcomers starting with traditional archery is buying a bow that is too heavy for them. Bows are rated in draw weight which is the force required to draw an arrow back 28 inches. If you draw the arrow over 28 inches then the draw weight will increase by about three pounds per inch and a shorter draw will decrease the draw weight by three pounds per inch. I suggest that the new archer stick with a draw weight of 40 to 45 pounds as anything heavier makes it difficult to maintain a full draw and aim properly.
Although you can hold the string in your bare fingers it will not take long for the string to tear the skin from those fingers. Traditional archers are divided into two camps on finger protection either using archer's gloves or tabs. Both work and I suggest you try out both to see what works for you. There is a third type of finger protection called a thumb ring, used in the eastern style of archery, but that is best left to experienced archers.
You can carry your arrows in a quiver that attaches to the limbs of the bow or in a more traditional leather quiver that is slung over your back or attached to your belt. This is a personal decision as all types work. Most hunting quivers are the bow or back style while side quivers are most commonly found on the target range.
I strongly suggest that you find an archery mentor at your local archery range who can guide you through the proper shooting forms. This is the single most important thing that you can do for starting with traditional archery and becoming a better archer faster.
Yeah, and don't forget to have fun, its all about fun.