I'm not going to recommend a specific rifle, especially since you're a lefty. I'm not certain what's available in left hand but...
I would strongly recommend that you look at a .30-06 chambering. Interesting from me since I'm a .270 Win. fan but a 180 gr. premium bullet out of an '06 definitely does moose in. I've been there & seen it several times. This even better since you have the capability to reload for it. It's an easy cartridge to load for and very versitile. I've been with guys who put moose down at about 300 or so yards with one with no problems. Later on you could go to a larger caliber such as a .338.
Just my thoughts & good luck.
Bear in Fairbanks

"Unless you're the lead dog, the scenery never changes."
Amazingly, I've lived long enough to see a President who is worse than Carter.
And finally,
Gun control means using two hands.