If you want a Mosin with maximum battle action, get a pre-war Finn. These are mostly M-27's, M-28's and M28/30's, with a mix of early model M-91's as well. When Finland felt the Red Army's hammerstroke in 1939 they had to call up every possible asset, including pretty much every Mosin in the country. A very large percentage saw action from what I've seen, and many have notches and other trench art showing time at the front.
When you get into the M-39's, M-30's and late model M-91's you're moving into the Continuation War and the Lappland War, by which time the arsenals were much better equipped and there was less reliance on the bolt action rifle. This is one reason why so many are in near mint condition. Also, some were made as late as the 1970's.
Among the Soviets, the best bet is a pre-war 91/30 or converted Dragoon. Most of these were rearsenaled but I've found some that weren't. Like the Finns the Soviets relied most on their bolt rifles early in the war. By the later time period there was a much greater array of small arms to choose from including some really fine submachine guns. Many of the late model 91/30's seen less aggressive service. And they were pretty poorly made to boot.
The reason the 91/30 stops when the M-44 starts is because the M-44 was never intended as a carbine like the M-38. It was designed from the getgo as a replacement for the 91/30. Though of course the SKS-45 and AK-47 came along to take up the main role as frontline rifle shortly thereafter.