At your point of arrival in Russia you have the option of completing a customs declaration form, where you can list any foreign currency and valuables you are bringing into the country.
If you book a tour through a travel agency back home, you shouldn't have to worry at all about visas and registration.
Moscow came high on lists of the world's most expensive cities, and foreign visitors were often shocked at the prices charged in restaurants and hotels, by airport taxi drivers, and in supermarkets selling Western produce.
The first consideration for most visitors coming to Russia is, of course, the weather.