In this page I will compile all the services I use and recommend to organize a trip to Russia.
1. Russian Visa
The cheapest and fastest way to get an invitation letter to Russia is through HotelsPro, a Russian company registered as a tour operator, whose main business is based on the issuance of letters of invitation to Russia (visa support). Through HotelsPro you can get a letter of invitation for 800 rubles (about 11 euros) in a fully automated way: http://hotels-pro.ru/order/visa-support.
2. Flights to Russia
Momondo is the flight comparison site I use to know which are the best plans and the cheapest way to travel to Russia. The great thing about its flight search engine is that it shows airfares without charge or additional fees, and allows multipath searches.
3. Trains in Russia
In recent years, there have emerged many intermediary private companies offering tickets for rail travel in Russia, either to make the journey from Moscow to St. Petersburg or the Trans-Siberian. However, the less expensive way to do it is precisely by avoiding intermediaries, through the official website of the national company of Russian Railways (RZD).
4. Accommodation in Russia
To stay in Russia there are basically two options: hotels or apartments. Ostrovok is an excellent Russian platform (similar to Booking.com) that will allow you to book accommodation, according to your budget. On this platform you will find very good deals to stay in Russia, better than those you can find in Booking or in other platforms.
5. Taxi in Russia
If you want to book a taxi online in advance to move from the airport to the city downtown or from any other location in Russia, an excellent option is offered by the Russian company KiwiTaxi, which allows taxi bookings not only in Russia (Moscow, St. Petersburg, Kazan, Vladivostok, etc.) but also in cities worldwide.