In order of importance:
1. Good suppressor cover. You won't be able to see very well once the can heats up after a couple of shots. Armageddon gear, Cole Tac and Burn Proof Gear are some of my favorites.
2. Ballistic Computer. Apps such as Geoballistics, 4DOF and AB Quantum are great and will serve you well getting started. A kestrel is the gold standard and has stood the test of time. The Geoballistics app has a cool GPS map feature that will give you a pretty decently accurate range to a target if you can pick out a landmark or can physically go to the targets to mark them.
3. Shooting bag. A sand filled Game Changer will work well for 90% of positions in a match.
4. Dope Card. Arm board, painters tape... anything to write down your holds for a stage. I like the Cole Tac cheat sheet V2.
5. Chrono. it's nice to know what your ammo is doing, if you get into reloading you'll definitely need one. If you have other shooting buddies, this can be a shared expense. Garmin Xero is the bees knees.
6. LRF/Binos/Spotter + Tripod. Put this toward the end because of the expense ($1000-$5000). Mostly needed at a PRS match, don't really need to just go shoot long range. But at a match, everyone in your squad will have a setup and will let you look through theirs. It's also the best way to get behind lots of different glass in conditions that matter. You'll be able to see why the expensive stuff is expensive.
Like others said, any backpack you can fit all your crap in, don't go buy anything nice and expensive until you figure out what you really need to carry.
