Shovel, make sure it's a metal shovel. I prefer the T handles as they are easier to stash in your pack and work just fine.
Probe, 300 cm probe is what you are going to want to get. If you run into a burial situation out there, there is a good chance it's going to be deep. A guy was rescued a few years ago at Baker due to the fact that a 300 cm probe just barely stuck him.
Beacon. I have my preferences but here is the rule of thumb. First off get a digital beacon. They are way better than analog beacons. Second, when getting that digital beacon get one that is a 3 antenna model. Pieps DSP, Ortovox S1, Ortovox 3+, Ortovox D3, Mammut Pulse, BCA Tracker 2 are all three antenna beacons. They all have their quirks and do some things better than others, but all will do their job adequately when called upon. You just need to practice with them.