Anecdotally, the professor of my algorithms class had us all sort cards manually and asked us to describe the algorithm we used when we began studying sorting algorithms. Most of us used either selection sort or insertion sort.

I would think bucket sort (into the suits) would be the most common. Whenever I am sorting named papers I always do it with 26 piles.

A-K in 13 piles then suits in 4 piles is a little faster. Or if your space limited you can group A-7 then 8-K.

That's more or less radix sort, no?

Yep, though radix and bucket sorts are closely related.