Welcome, I just relocated out here in July...
The permit to purchase question was mostly answered, except for one thing - you won't get a temp license from the DMV..at least, I didn't. They just punched a hole in my NY license. As a consequence, I didn't get my license number for quite a while..a couple or so months. I had to wait for that to come in before I could get my permit to purchase, which requires the DL number. So, it may be a few weeks/month/etc before you can buy a handgun and/or "assault-type" weapon. (Some things fall under needing a permit to purchase to buy, like an AR, etc.) But, you can still buy long arms that aren't restricted like bolt guns and shotguns and whatnot.
As far as where to live...*shrug* Depends on how far you want to drive to get to work and etc
I have a good realtor here I can hook you up with; he'll take care of you right. Me, as I had never bought a house before, found him to be an invaluable resource, especially for moving out here...
Me, I live a cool 35 miles from work, about 45 minute drive in to Minnetonka, where I work out of. Being from NY, this is a "normal" commute time for me...and as a consequence, I live out in the middle of nowhere, with a monster lake and a golf course both within walking distance of my front door. (And horses and cows) Me, I like being out in the middle of nowhere.
As you're on the east side of the cities, Wisconsin is an actual viable place to set up shop. The upside to WI for our hobby is that it's a C-III friendly state..the downside is that there's no CCW (but there is open carry)...and if you work in MN, I don't think MN grants non-resident carry permits.
(The reason I say it's a viable place is that a friend of work lives out in Hudson WI, and he hauls in 50 or so minutes to work in Minnetonka...so it's not too horribly bad.)
Unless you're a city guy, don't discount 15-20-30 miles outside the city...