I too own and shoot both the 96 Swede and Nagant, models 91, 91/30, 38, 44, 56(?) and Finnish 39. Sarco has some target grade 96's, some of them are capable of excellent accuracy. Gunsandammo.com has Finn 39's, with a cracked stock, for $99.99, delivered. All of the 39's have excellent bores and they shoot as well as my Springfield Armory M1.
The 39's are ugly, this si no other word, the metal work is rough, the triggers vary from hateful to fine, although there are several drop-in replacement triggers available and with the single stack magazine they can be difficult to carry in a one hand position.
The Swede 96 is definitely a better candidate for upgrading, customizing. 96's have fine metal work, an excellent two-stage trigger and the 6.5x55 cartridge is capable of taking any thing that walks, crawls, grows feathers or sheds blood in North American. Consider that one of the ivory hunters used 6.5 caliber to harvest several hundred elephants. If you do your part, the cartridge is capable do doing its part.
My personal choice would be one of the Finn 39's from Gunsandammo.
Lapetit