Here are my favorites:
Raspberry: 
Latham: early season ripening, hardy, cold tolerant and 
Heritage: Mid Season ripening and longer lived plant.
I have personal experience with Heritage and find I get 2 crops per year.

Blackberry: Illini: vigorous but thorny plants

Raspberry and Blackberry plants will require ongoing care; fertilizing, pest and disease management and pruning. The reward of a fresh crop of berries is worth it all!

I have included a link to a couple of information / data sheets with descriptions of the raspberry and the considerations of each.
https://www.canr.msu.edu/uploads/files/AABI/raspberry_variety_factsheet-final.pdf

This publication is from Penn State Extension and has great information that would still apply to our West Michigan climate:
https://extension.psu.edu/home-fruit-gardens-table-7-1-recommended-raspberry-varieties-for-pennsylvania 

MSU Extension has this great bulliten with considerations for all home garden fruit growers:
https://www.canr.msu.edu/news/considerations_for_growing_backyard_small_fruit 

Univ of Maine has a great publication on how to grow and care for brambles:
https://extension.umaine.edu/publications/2066e/#suggested-varieties

After reviewing the information provided, should you have questions feel free to write back.

Have a great day!