Beacon, shovel, probe, and an adequate pack to carry your gear (in addition to the avy gear think lunch, water, extra layer, and board carry) with.
An Avalung is a nice extra. I have one that I wear everytime I am out. Not needed, but if you get buried it could make the wait a whole lot more pleasant. Another option is to get an airbag
. Those things work. The survival rate in an avalanche with airbag users is over 90%. You just don't get buried when those are deployed. Pricey though. I don't have one, but in a year or two I probably will. Xavier De La Rue was in a monster avalanche, the type that no one survives, and deployed on of those. He pretty much walked away from it. Amazing.
Snow sense is a good book, but the n00b I'd recommend Bruce Tremper's book "Staying Alive in Avalanche Terrain
". Bruce is a fairly entertaining writer and lays out the basics in a simplistic easy to understand way. In addition he is one of the top 5 avalanche guru's in the world. Then again so are Jill and Doug. Definitely get a book and read it. You'll be that much more on top of the game when you take your avy class.
Splitboarding is easy. When in ski mode for skinning, it's pretty much like having big snowshoes on. Don't stress over it.
For a beacon, make sure you get one that has three antennas and that it is digital. Do not buy an analog beacon. Analogs take too much practice and I'll smoke anyone using an analog beacon with my digital beacon. Plain and simple. Three antenna digital beacons make pin pointing way easier. The Pieps DSP, Tracker 2, Barryovox Pulse, Ortovox D3, and Ortovox S1 are all three antenna beacons. In the class I lead a few weeks ago, everyone in the group went with the hype and had the BCA Tracker, a two antenna beacon. One guy had a Pieps DSP. When we went to beacon practice, the guy with the DSP and 4 others had never used their beacons to search. Two of them had experience with their Trackers. The guy with the DSP absolutely smoked everyone with the tracker. Pinpointing was super quick because of the third antenna. The best beacon is the one you know how to use, so practice with whatever beacon you get a lot.
After you take your level I, get a crew going and get out there and practice, often. Field experience is where you'll gain the wisdom and knowledge to be a savvy back country user.