Much experience at this moose lotto system (that was difficult for me to admit.....since I haven't drawn anywhere as of yet!)
Focus on the NE states for now......the odds of drawing in the western states seems to be somewhere in line with hitting PowerBall when the jackpot is upwards of $350 million!
VT may actually have the best odds (use that term with a smile on your face). Apply in ME and NH as well. Ya never know.
Now lets focus on a location where the odds are really not all that bad.......and it's not in the US...but it's close....New Brunswick! While the numbers may not be totally accurate, they will give you an idea of the odds to draw a permit. It seems the average number of applicants for non-resident moose permits is around 1300 applicants for around 130 permits, give or take for a particular year. Anyhow...you do the math....none of the states can match those odds. Unlike the states however, you will be required to hunt with an outfitter. There are quite a few just over the borders with Maine (think NB bear hunting camps). Its only a 3 day season, but you usually book for a full week and do some scouting and fishing. Being forced to use an outfitter is what turns most people off about Canada, but, overall, if you draw (I have not in 5 years) it's still a relatively cheap guided hunt. Note that there seems to be a very wide variance in what these outfitters charge. Getting a moose hunter seems to be an added benefit for these lodges since they main focus is really bear hunting and deer hunting.
I started applying for moose (and sheep) in various western states when I was much younger. I gave up on WY after a few years based on feedback from some locals ("lost cause"). Not long after that I stopped applying in all the western states. I've been applying in ME the longest (since we own property there), along with the other states for quite a while. I'll keep applying until 1: I draw, 2: I break down an book a hunt in Quebec, or 3: I retire in about 5 years and move to AK.
Good luck to all you fellow moose lottery addicts!