Don't buy grass seed from a big box store, or any kind of national chain. My reason for this is that these companies tend to include some of everything so it will grow from southern Arizona to northern Maine. What you wind up with large percentages of the seed being totally useless for your area. If you go to a
local seed nursery supplier and buy from what he sells bulk he'll have what grows in your area.
Here in SW Pennsylvania we use a local mix called Penn State Mix, well what else!!! It's a combination of mostly
Perennial Rye grass a small amount of Blue Grass and a fescue. None of these seeds would likely be a good mix for say Florida. So I'd say your local seed/nursery supplier will know best what you need. I have in the past amended the mix that's best for my area by adding a small amount of a high quality Blue Grass, which I might think might also be suitable for Minnesota?? Where I buy he has bins and empty bags. You scoop what you want, don't mix seeds in your bag. Tie a piece of rope around the plastic bag. What I did was buy a small amount of a quality seed and mix it later. If your location is a rental or a short term stay then don't go to this extra bother. I'd cover the seed with a very small layer of
mushroom manure. I shake some off a shovel very finely. Then
water on a very fine spray. Keep it damp, but not soaked. Perennial Rye comes up in a week the others I mentioned will take about 3 weeks. It'll start sprouting here in March, probably later in Minnesota? You can do this now, but some will say it's too early.
Don't use Peat Moss to cover the seed with. For one, it's not popular here, but more important it's so dry and light that when it rains it floats away.
But if your seed mix contains only what's appropriate it winds up being cheaper.