I am no expert but I dove into the trad world head first a few years back and I am loving it! I now fletch my own arrows, make my own bowstrings, quivers, fletching, tabs, armguards and I have one Osage longbow under my belt. Trad hunting and trad DIY is addicting! Anyways, here are my thoughts.
I killed two deer last year with a 38 pound recurve and one with a 40 pound longbow. All three had exit holes. With your draw length (which is probably around 27 since you are 27.5 with a compound) you are probably shooting around 42.5 pounds. In my opinion, that is a great hunting draw weight.
If you are looking for regular carbon arrows or shafts, Lancaster sells the Gold Tip Warrior. It is a good inexpensive shaft. If you are looking for a carbon that is imitation wood, the Gold Tip Traditional are a good option. Wood and aluminum arrows can work great as well, but I have limited experience with them. If you settle on carbon, I would recommend starting with a 600 spine, but 500 might work. I would use a 100 grain brass insert and a two blade broadhead of your choice. I would recommend the Magnus Stinger unless you enjoy sharpening things then a Zwicky, Bear or Grizzly. Start with a bare shaft and cut the nock end down until its flying straight. Then fletch it up or have it fletched. I like to end up with an arrow that lands between 10 to 12 grains per pound so in your case 425 to 500 ish total grain weight. The MOST IMPORTANT thing is that you get your arrow tuned to your bow and flying really straight.
With that much draw weight you will need to limit your range. With my 40 lb longbow I keep it under 20 and prefer to set up for a 12 yard shot. With Trad equipment your shot angle becomes more important, so try not to hunt too high in the tree. I like to sit between 12 to 17 feet depending on cover. If you need a quiver I recommend Big Jims bow quivers. Since you already shoot the bow well you are way ahead of the game. Enjoy the challenge and good luck!