I have made my own bows but no arrows yet. Osage is about the best bow wood there is but can be difficult to work with for a beginner. I find White or Red Oak to be a bit brash for shorter long bows but pretty decent for longer ones. Hickory is one you can't go wrong with in my opinion. It is tough and forgiving of small mistakes. Dogwood is another one but it can be hard to find a suitable piece of Dogwood. The tree usually grows all knarley and twisted and you need straight grained wood for a bow. However, if you do find a suitable piece of Dogwood, it is very elastic and tough and is a good choice. It is also extremely white wood and takes stains very well. Stay away from any species of Willow or Birch. They are not good bow woods in my opinion.

As I said, I haven't made arrows so my advice here is of limited utility but I would go with goose feathers for the fletching as they are naturally water proof. I would like to build my own one of these days but just haven't yet. I have looked into using bamboo or river reed shafting and that looks very promising; sort of nature's carbons if you will. They are very light and strong. I have read that wild rose bushes are a good source of arrow shafts as well as dogwood. The challange (at least for me) is finding a reliable way to measure the spine. Knapping arrow heads is another challange alltogether. It may take a while to get proficient at knapping. I do know that quartz can be used but it has to be heat treated first for some reason. I was told to build a good fire and place my quartz in the middle and let it heat for some hours. Things like bone can be used too. Bone heads are tougher but not as sharp. SOmeone above had a good idea with turtle shells. I imagine they could be processed more easily and could be made quite sharp. The shells of large freshwater mussels might be used too.