Hi! I recommend you to go from St Petersburg to Moscow by fast train Sapsan. It is comfortable, quick and much better than bus. I myself often travel by this train and I like it! Some words about cities. I think, St Petersburg is much more interesting and beautiful than Moscow. So you should stay there minimum 1 week to see all must see attractions in the city and suburbs.
And it would be better if you have a guided tour. This way you will save much time and spend great time in the city! By the way, I can recommend you an excellent professional English - speaking private guide in St Petersburg. Just let me know!