$200 at this time of the year in Michigan probably ain't gonna happen.
With the exception of really high end machines, almost all of the used ones that you'll find were manufactured by MTD and have Tecumseh engines. They're given different colors and brand names, but they are all just larger or smaller versions of the same thing.
Last year, I owned a Toro 6.5hp, a Craftsman 5hp and an Agway 5.5hp with tracks. They were all essentially the same.
Tracks can be helpful, but a tracked machine is hard to move around on dryer pavement because you need to slide it a bit to steer.
If you're shopping in the $200 range, it's important to understand that if you buy a fixer upper, you can't just go to Tractor Supply or Northern and get any horizontal shaft engine and drop it in place. The Tecumsehs have a second shaft that rotates off the cam in the opposite direction. One drives the wheels and the other drives the auger.
Also, don't replace the shear bolts with regular bolts. That makes things get expensive. Always have some spare shear bolts on the shelf.
The electric start snow blowers don't use a battery. The have a starter mounted on the engine but you have to plug an extension cord into it. If you lose power in the storm, you're gonna be pull starting it.