There are quite a few pretty accomplished skiers here who have gotten out on the Brahma SP (CA) and were duely impressed with what it was capable of. As far as it being able to handle powder, it wasn't too long ago that an 88mm ski WAS a powder. ski. The Brahma is a good foundation ski for you, and if I was going to choose one width of a ski for Tahoe it would be a ski in this range. You can always add a wider ski down the road but I would not go much over 95mm for what you need and where you are in your skiing career. While you might not be ready for this Olympics, you will surely be ready for the next one.
I gave a pair of Bushwackers (basically an older version of the Bramha SP) to my son's race coach a couple years ago. As you can imagine, she can ski. She has raved about them more than once. I looked up an old text from her "I don't know what it is about those magic skis you gave me but I'm crushing it and my knees dont hurt!". That $400 deal for new skis and bindings is legit, I'd go for it. For your size you could go 166, 173 or 180 but I'd probably go with the 173 with your description. With the shape and profile, they will work fine in powder.
These will work in the park but stay off the rails so you don't trash your new skis (an post yourself). As for "trying backcountry", you should have probe, shovel and beacon on hand and have taken Avi 1 class before going outside a resort.