Now I'm not an archer, but I got plenty of archer friends so I know a thing or two about larp archery. There are a number of things to consider about it, since it may not really be your thing and it involves a higher monetary cost than simple sword fighting. That should not discourage you of course and if you are serious about it, go ahead.
First thing to consider is the bow. You COULD try to make it yourself but pvc bows look dumb and making a real wooden bow takes experience, tools and materials that almost all of us lack. Therefore its easy to assume that when looking for a bow, the obvious choice is to buy one. For a newbie, a junior bow such as this one
is a nice start. These and similar junior bows come at about 30$ apiece and if you find out that archery was never really your thing, at least you'd save some money. They are also readily available in hunting/weapon shops and sports goods stores. If you like being an archer though, there are better options(more expensive ones too). You can buy a recurve replica online for 100-200$ and you will love it. Keep in mind that your bow should not exceed 20-25 kg of strength and that the high end is only for experienced archers.
Next thing to consider is the quiver. Due to their shape, larp arrows take more space and be a problem to manipulate. Its easy to fumble and spill your arrows on the field. Some people solve it by stacking their arrows upside down, other arrange them carefully. Whatever you choose, practice it first. Good thing about archery is that unlike sword fighting you don't need a buddy for real training. I might talk about this more later on, I need to refresh my memory on the subject.
Last but not least come the arrows. I'd suggest you buy the cheapest fiberglass arrows and that you buy them in bulk. You should start with about a dozen and be prepared to lose one every couple of games at the very least. Sometimes you'd lose more. There isn't much you can do about it, You'd send it in a tree, the nooks will break off, the feathers will fall off, someone will step on it...Losing arrows is a 100% certainty and a constant budget drain.
When making your arrows, pay attention. There are a dozen or so larp arrow guides in the net, but I guess another one won't hurt. Besides I'll mention a few specific points that might be useful.
Always cut off or saw off the arrow head. That is a must. No exceptions.
Some folks and some larp games insist on using a coin to block the tip. I find it a bit unnecessary - if you are using a bow that can pierce through the bottle cap you are doing it wrong in the first place. However if its in the ruleset - use a coin to be 100% safe.
Sometimes its a cork, but plastic bottle caps work just fine and are far more readily available. DON'T just remove the tip and add a foam ball. The arrow shaft WILL penetrate through the foam.
Some Aluminum tape will give it a more distinct look, and the shine will make it easier to find. If you have any bright coloured tape(orange, red etc.), use it.
Aand thats all folks!