Foremost is a Farmer's insurance company. Foremost is the "special lines" (m/c, boats, etc) arm of Farmers.
Progressive started out as a high-risk carrier back in the 1930s if I remember right, and has progressed into a major player. Progressive is the largest insurer of motorcycles in the country, or was when I was there. Progressive was very proud of their special lines coverages and claims handling and trained their claims adjusters in special lines like no other insurance company I've heard of. A Progressive claims adjuster would be trained to identify damage as well as, and probably better than, anyone in the industry.
That doesn't necessarily mean that Progressive is a better overall company, but in my area, if I wasn't going with through the same company as my home owners policy (for the discounts) I'd have Progressive Insurance for my motorcycle (based on claims handling).
I've worked as an adjuster for both Farmers and Progressive.