Kristine, Congratulations on your purchase. I also do SFR in Minnesota and am currently in the process of finding and approving a tenant. I would highly recommend "Landlording on Autopilot" by Mike Butler. He has awesome tips on landlording.
Here's an example of how I do it.
*List the property and include as much detail as possible without getting to wordy, include the rent and monthly income they must make to qualify, usually 3X the rent. This helps eliminates a lot of unnecessary phone calls.
*Find a good pre-screening worksheet that you can use when taking phone calls. ( might be a good one in the forms on BP) You can eliminate a few more potential tenants this way. Ask questions like, Do you smoke inside or outside. Don't ask if they smoke, they alway say no. How many adults, how many children, (state laws vary but most only allow 2 people per bedroom) If you have a two bedroom and 6 people in a family, you can eliminate them right away. Do they have first months rent and security deposit available right not. Do they have good land lord references.
* Schedule a showing and try get them all to show up 10-15 min apart. This save time for you and your current tenant.
* Have applications available at the showing. I let them fill out the apps there or they can mail them in. I have them enclose a check for $35.00 per person for credit and background checks with the application. Watch to see if they remove their shoes, smell like smoke, dress nice, walk them to their car, is it clean? You can tell a lot just from observing.
* Once I get an application, I read it over carefully, make sure the time lines work. If there is a gap in where they lived for a few month or year, are they trying to hide a bad landlord reference. Don't call the current landlord first, it might be in their best interest to get rid of the current applicant so they might not be truthful. Call the one previous, they are the best. Contact the current employer and verify the income, once you have covered all that an everything still looks good, now its time to cash the check and do a background/credit check.
*At this point you either accept the tenant or you send a letter of denial explaining why. If you denied them go on to the next application and repeat.
If you accepted the first applicant, return any checks from other applicants explaining that the vacancy was filled.
Keep a file for each tenant with all the paperwork involved with this process.
I also keep the paperwork (prescreening worksheets) on the contact in case I have a vacancy in the next few weeks, I can always call them back with out advertising.
*Do you research on what you should keep and have on hand in case of a lawsuit.
* My realtor also has rentals, so that has been a good source of information for me.
Good Luck!