I have 2 M44s, and an M38. One 44 and the 38 have been converted to a more "modern" style with synthetic "monte carlo" style stocks, and the 38 has been "kit" converted to a WWII style sniper setup (the teeny little scope, the reworked bolt). The 44 I was going to fit for a normal scope, but havent gotten around to it yet. The other M44 is in original condition, with the cleaning rod, a belt "clip" pouch, a handful of the metal "clips" (I have no idea what they are called) that hold the bullets together for quick loading into the clip area, and the bayonet (I removed the bayonet from the other "modernized" one).
I did have problems with some of the military surplus ammo I found at the gun shows, but only in that it was not as accurate as I would have liked, and very "dirty". Winchester makes some very affordable modern hunting rounds in 7.62x54 that are (I believe) Noslers. I took a deer at around 75-80 yards with the M44 and the plain iron sights, very accurate.
The only suggestion I have if you decide to go with one of the synthetic stocks, they arent perfect fits. You have to do a bit of sanding here and there to get the barrel to seat right. Otherwise, all the guns are shooters, all work flawlessly, and all were very inexpensive.