7,62mm is, indeed, 30 caliber. However, that refers to the bore (land) diameter, not the groove diameter. The Europeans have some different ideas about how the relationship of land and groove diameters should be, and these groove diamters will run large, by our standards.
Most of the Russian and Soviet-bloc rifles will run 0.311"-0.314," so larger bullets are in order for those rifles. I use bullets of 0.311" in my Soviet Mosin. Typically, bullets for the .303 British work well, so look around after you measure the groove diameter.
I have a Finnish Mosin, whose groove diameter is 0.311." The Finns produced rifles in the 0.309" range for a time, but reverted back to the 0.311+" diameter for WWII. That means one should measure the groove diameter for those, too.
If you buy an arsenal reconditoned rifle, one of the Soviet rifles redone there, even the bore will have been reblued. The bore will look terrible and dark, but will eventually brighten up some as you shoot and clean it. Many of the Soviet rifles were couterbored at the muzzle to remove cleaning rod wear; those rifles do not always shoot quite as well as those without a counterbore.
Lapua makes some really good target bullets for these rifles and if you can get a Finn with a .309" groove diameter, they shoot very well, indeed.