Lots of good info from other posters. I'm sure someone with far more extensive knowledge than myself will be able to further assist you, but here are a few of the basics to look for:
Basics:
1. All matching (preferably including a bayonet)
2. Good bluing with no noticeable rust
3. Good crown and bore (a small flashlight is a great tool here)
A little more advanced (for collectability):
1. Finnish (SA stamp - usually quite expensive, but sometimes you get a good deal)
2. A Russian carbine - particularly the M38
3. An ex-sniper (look inside the receiver for small circles - these are from the plug screws they used to plug up the sniper mount holes, an ex sniper should afford better accuracy)
4. "Hex" (octagonal) receivers are generally of better quality (expect to pay a little more for these)
To sum up, if you're just after a good shooter, look for the 3 basics and possibly that it is an ex-sniper. If you come across one of the other characteristics, at a reasonable price, it can be well worth picking up. If you're after more info, this video is pretty good:
https://youtu.be/TV2MSou_CS0 (What makes a Mosin rare by Iraqveteran8888)
Hope this helped!