Official currency is Ruble, which you most likely won’t be able to obtain outside Russia. The rate has been kept quite stable during last few years (1 USD = 28...30 Rub; 1 EUR = 34...36 Rub). You can check official rate of the Central Bank of Russia - all exchange offices vary no more than +/- 1% from these numbers.
All former USSR republics now have their own currencies, which may vary a bit more. While it is possible to get these currencies in Russia, the rates are much better in their home countries.
If you intend to spend most of the time in the countryside, then the best way to bring money to Russia is cash, preferably in US dollars. The second best way is also cash, and the third best is cash again. Travelers’ cheques can be exchanged and credit cards can be used for payment in large cities, but once you’re outdoors, forget it. US dollars can be changed easily in even smaller towns and often can be used (and even asked) as a payment for long taxi rides, private transport or accommodation and other non-official services.
Prices are typically significantly lower than in the west, especially for public transport and food (this does not apply to 5-star hotels and limo rentals in Moscow though). A day train or bus ride would cost in a range of $5-10 and the daily food allowance would be no more than $5-7. A private vehicle (that comes with driver) can be typically found for $30-50 per day.