"The Finns never made a Mosin Nagant rifle."
The Finns most assuredly made rifles. They did not make receivers and many other parts, such as butt plates or magazine parts, as they had many, but they made rifles. An M39 might have a Russian, French or American-made receiver, but it will have a Finnish-made barrel, front and rear sights, and stock. It may also have bolt parts that were Finnish (my SkY had a SAKO extractor and cocking knob) and the trigger will be either Finnish manufactured or modified.
Even on the broader sense, they manufactured whole rifles at SAKO, Tikka, and VKT (Valmet), and continued to manufacture Mosins into the 1980's. Indeed, the Finns manufactured Mosins far longer than the Soviets (though the most recent Mosin model manufactured was the Czech VZ54/91 from the 1990's).
As far as getting a Mosin, any refurbished Mosin will be as good as another. If you keep an eye out, you can find some that were sniper rifles at one time by inspecting the bolt raceway for welded mounting pins. Even rough wartime examples had good barrels and internals, with the only corner-cutting being cosmetics. As far as cheap shooters, that is how I would go. There are others, of course, the Finnish models are among the best ever made (an M28/76 is the cream-of-the-crop in currently available rifles, the TKIV being the holy grail).
But, you want nice? The best M91/30's were made by Tikka and are around. M39's are superb as well. Indeed, most Finnish Mosins have excellent triggers, excellent stocks, etc. The M28/76 with D166 stamp is about as nice as they come. They are pricey, but man.
The top one is 100% Finnish military (the bottom 100% Czech).
http://www.thehighroad.org/attachment.php?attachmentid=175182&d=1353679109