Moving here isn't tough, this is the Midwest after all. You can expect a credit check to be run by most places, but don't sweat it as it is generally just a formality. References from your previous landlord and proof of income will help mitigate any black marks on your credit file. Be ready to hand over both a security deposit and a pet deposit if you have pets. Most places don't require a monthly additional hit on your rent for having a pet.
The neighborhood issue is mostly a real estate designation here as there is no real difference except in the cost of buying a house, and even then it's within negotiating range.
Savage is a suburb of Minneapolis, so most people who live there like to spend time in the big city for work and play. The cities are connected by Route 444, where residents can hop in their cars and get back and forth quickly. There is also bus service between the two cities.