Top to bottom: Mosin-Nagants 1891, 91/30, 1938, 1939 (Sako), and 1944.
Just as western Europe was dominated by the M98 Mauser and its variants, much of eastern Europe and Asia has been dominated by the Mosin-Nagant and its decendents. Once considered a "junk" rifle, many shooters have changed their minds about the Mosin-Nagant in recent years, due in large part to the release of top quality war stocks from both Russia and Finland.
The earliest model, the 1891 or M91, was produced in Russia and in the United States. These are no longer available on the surplus market, and having been through two world wars and a revolution, even when found they are usually not in "competitive" condition.
There is a Russian Mosin-Nagant rifle slightly shorter than the M91, and this is usually refered to as the Model 91/30. These are available in many grades. There is a similar Finish Mosin-Nagant rifle called the M39. These were made from captured 1891 and 91/30 Russian rifles which were reworked by Finland, and these are generally considered more desirable.
A shorter version of the Nosin-Nagant was produced by the Russians for WW II, and is usually refered to as the M38. They are often offered in "excellent" to "unissued" condition and with a choice of manufacturer.
The last model of the Mosin-Nagant was the M44, which was produced in Russia and in several other Soviet block countries. Again, various grades are available and you tend to get what you pay for. A Mosin-Nagant-type carbine manufactured in China has appeared on the market, but we do not have enough information to write an evaluation.
Mosin-Nagant rifles were chambered for the 7.62x54R cartridge. The cartridge seems to be capable of excellent accuracy, but suitable ammunition can prove expensive. The surplus military ammunition coming out of the old Soviet block is not suitable for match work and is only slightly less corrosive than battery acid. The brass used to load modern S&B 7.72x54R ammunition does not seem to reload well. Prvi Partizan ammunition does not perform well, but provides usable brass. That leaves brass from Norma or Lapua, one hundred rounds of which can cost more than the rifle. This should improve in the near future if American-made brass becomes available. Recently we have reports of Winchester brass being offered for sale, and Winchester ammunition should be available again once the market recovers from its Obama-induced panic.