Chris,
Welcome to Idaho.
First of all, as you seek advice beware of the bitter people who respond about it not being like the good old days. If you haven't hunted elk before it will be a pleasure to live in Idaho. While the Wolves are making it a lot harder all the time, there are still a lot of elk in Idaho, though not many that score over 300. But, any elk is a good elk and frankly young cows and bulls eat better anyway.
Here the system is that most regions's have some units that have ample over the counter tags. I mostly hunt SW and Central Idaho, but I believe there is plenty of opportunity up north. As long as you don't plan to apply for any of the three TROPHY species(Sheep, Goats, and Moose) then you can apply for Controlled Deer, Elk, and Antelope and if you are not successful you can buy General Deer and Elk over the counter. Antelope is draw only, unless you want to hunt with a bow. No Antelope up North either.
The biggest bummer is that you won't be considered a Resident until you have been here for 6 months, so you may want to wait until that date an then buy OTC tags as that will save you a lot of $$.
Go on the F&G website, they have good online tools for general research. Get Google Earth on your computer and start figuring out just your rugged this state is.
Once you get here simply start chatting with people, but don't expect very direct info, pleople work hard here to scout and figure out the country, but you will get some help. Then start scouting. By April, at least down south, the elk will start migrating back to Summer Range then you can start to scout when the snow recedes enough.
Good Luck!!