For the first part, it needs to be "two types", because there is more than one type.
For the second part, I'm "99%" sure it needs to be "soldiers".
Regarding "types" vs. "kinds," I think those are interchangeable and do not differ in meaning in any discernible way. Either way, you're dividing up all soldiers, putting them into buckets, and putting a label on the buckets :-).