In general stream trout season doesn't open in Michigan until April 27th, and Bass not until May 25th.
You can go after certain trout and salmon in certain rivers during the winter though, but there are some closures, and rig restrictions.
Regs are here:
https://www.michigan.gov/documents/dnr/2019MIFishingGuide-Feb26_647890_7.pdf
That being said to do all of the things you want and more I would suggest the NW side of Michigan specifically from Ludington, up to Traverse City. Lots of great fishing, including some of the year round rivers for salmon and steelhead. Tons of land to roam with trails galore including a large chunk of the North Country trail. I have a place outside of Manistee in the Huron National Forest and love that area. It isn't as touristy as a lot of the areas up that way, but there's plenty to do, and plenty of supplies available.
Any questions feel free to ask. I'll subscribe and check back, or just message or email me.