Correction: given that you plan to "flit around a bit" in Russia, you should get the tourist visa. I just posted my experience with it in the sticky on visas.
You only need a business visa if you plan to business activity in Russia. The tourist visa is cheaper. Just use an online agency to get an LOI to cover the dates. Know that you'll need to register your visa wherever you stop in Russia (hotels will do this for you), and have train tickets or something to account for the time in between.