If you want to be right in the thick of the bar scene and don't mind paying a little more: Wrigleyville, River North, Gold Coast or Old Town.
If you want to pay a little less, but still want to be in an area with a lot of options for going out/night life and you don't mind a few hipsters: Bucktown, Wicker Park, Logan Square, Ukranian Village.
If you want more laid back neighborhood but still withing good range of plenty to do but a little pricier: Lincoln Park, Roscoe Village, North Center.
If you want a more laid back neighborhood but a little less pricey and still within range of plenty to do: Lincoln Square, Andersonville, Rogers Park
If you want to be downtown but not pay the cost of Gold Coast, Streeterville or River North: South Loop or West Loop.
If you want to be in the suburbs, I'm not the right guy to give that advice.
As for tips for the first couple of months: Chicago is very friendly - go out and meet people. We've got a great Chicago A&M Club (it's on facebook). Go to Chicago Sport and Social (google it) and sign up with some random people to play a sport or go to a social outing. There's a bar for just about every sports team, so you can find your favorite team's bar and go meet other fans.
Be prepared to pay for a parking ticket or two if you have a car. No one knows the rules for a while - it's just part of your introduction to the city.
It's a great city - go out and explore it. Check out the museums, the parks, the boat tours. Read Devil in the White City for some great history so you can speak intelligently about your new home.
Oh and buy a good winter coat and boots. Don't go cheap on these, you'll use them a lot.
Welcome to town!