7.62x54R: Extremely inexpensive cartridge, Similar and energy to a .308Win. (significantly greater than the .35Rem.), have relatively good ballistics (fairly flat, bucks wind nicely), and are generally chambered in inexpensive firearms.
Conversely, it is also generally corrosive and good softpoint hunting cartridges are difficult to find and much more costly (but still on par with the .35Rem.). Additionally the rifles that is typically chambered for this cartridge tend to be surplus and have varying levels of quality (and accuracy), and tend to be awkward for hunting due to the difficulty of scoping the rifle, the weight, and greater perceived recoil.
.35Rem.: Slightly more capable than the .30-30 due to the larger bore diameter and increase in energy. Fairly common cartridge that is available at most gun shops (but not at Wal Mart, et al). Typically chambered for rifles that have outstanding handling characteristics (lever rifles), and are fairly affordable. The round also has fairly low recoil making it a great choice for a new deer hunter at short range.
On the other hand, the .35Rem. is a fairly low powered rifle, generally considered unsuitable for game larger than deer. It also tends to exhibit a poor trajectory partly due to the round nose soft points that are typical (Hornady LeveRevolution are a partial solution, but more costly). Ammunition is comparably expensive, but only when compared to 7.62x54R.
In conclusion I believe the Mosin is a good choice if you are looking for a rifle to plink with at the range, but a poor choice as a replacement for a hunting rifle. I believe that an inexpensive .30-06, such as the Marlin XL-7, would be a much better choice.