Traveling from Moscow to St.Petersburg

Hi there,

I'm planning to travel to Russia with friends and we intend flying to Moscow first to visit the city and then head off to St.Petersburg. We would like to go by train. I did some search in the internet and I can see there's a fast train what seems great, but I couldn't see the prices neither if the ticket can be booked online from outside of Russia. Could you please help? Thank you

In addiiton if you have good tips for hotels near the city center in Moscow (reasonable price), I would also appreciate your opinion. Спасибо :o)