The Premier is way too expensive and only has 8.5/32 tread, no good for heavy rain and snow. Also, keep in mind that even though BFG and Uniroyal are owned by Michelin, they're nothing like actual Michelin tires. (This does not apply to other tire companies because Michelin makes their tires differently than other companies, and BFG/Uniroyal are simply "other companies" that just happened to bought out by Michelin). Michelin tires aren;t made in BFG plants, and the Uniroyal and BFG's aren't made alongside the Premier, for example.
If you must stick with Michelin, get the Defender T+H or Pilot Sport AS3, with the full 10/32. The popular Cooper CS5 Ultra actually has 11/32.
Although you can use H-rated tires with no problems, most tire shops refuse to install tires with lower-than-OE speed ratings due to fear of lawsuit (but going higher is no problem). Note that it actually isn't illegal to install lower speed ratings, but most tire shops just won't do it. The Pilots SPort AS3 is available in V and also W speed ratings in your size
If you're using a single tire year-round, you'd be better off with something like the Vredestein Quatrac 5, Toyo Celsius, Goodyear WeatherReady, or Nokian WRG3. Even if one of these have an H speed rating, most shops would still be willing to install them since they are legally winter tires with the mountain and snowflake symbol
But first, decide whether you;re going to use all-seasons, or separate winter tires
EDIT: Tire Rack has the CrossClimate+ in the size 225/50-17, which is prefect for you, since they are probably well-suited to Michigan climate, and they are Michelin like you want, and have the V speed rating