A Nagant is an interesting piece of history, but I concur with others that it really isn't the best gun to learn to shoot a revolver with. Besides the quirks of the design which have already been mentioned, the cartridge itself adds another layer of difficulty to things. 7.62 Nagant ammo is neither particularly common nor inexpensive and there is simply no way of getting around the fact that to learn to shoot any gun well, you have to shoot it quite a bit. Even if you handload, 7.62 Nagant is a very quirky cartridge that requires a lot of patience and tinkering to reload. Honestly, if you really want to shoot a Nagant a lot, the best option would probably be to get one of the .32 ACP replacement cylinders but even those often require fitting.
At this point, something in .38 Special or .357 Magnum would probably be the best choice for a beginner revolver (.22's are nice, but the availability of ammo has gotten pretty spotty over the last few years). .38 Special ammo can generally be found just about anywhere that handgun ammo is sold and, while not as cheap as it once was, still isn't horrendously expensive. Better still, if you handload, .38 Special is very easy and economical to reload.