I have seen many foreign tourists travelling alone across Russia. As for the route, I think the way to Beijin via Mongolia is more attractive variant then long way to Vladivostok. However, if you want to get familiar with the Far East taiga and Amur tigers - your way to Vladivostok!!! On the way it is better to stay in the Ural Mountains, Tomsk (if you want tosee old russian wooden architecture), Baikal and Ulan-Ude. and then to Mongolia. The only problem is to buy tickets for train Moscow - Ulaan-Baator- Beijin.