We too are in Minnesota. We bought a house a few years back in Duluth (ok like 6 now) but when we did we did the first time homebuyer courses associated with the Minnesota Housing Finance Agency. I did a query on their website for the st paul area and came up with
this website
I'd recommend calling them for help in answering your questions. We took this 1st time homebuyer's course for ~30 bucks and it proved invaluable. They also ran our credit score at the time and suggested ways of improving it. And we have a sleeping mortgage (basically a second mortgage at 0% interest) for the closing costs that we don't have to repay until we sell or refinance the house.
MHFA also has on their website people who offer special programs for first time homebuyers.
Finally, one thing to consider in your price is the cost of insuring your home. When we paid renter's insurance it was on the order of 100-200 bucks a year. When we switched to homeowner's insurance it was more like 70 bucks a month.