Thanks again for all the feedback! I know I was told by my friend, who's a language teacher and tutor, in St.Petersburg, that there are opportunities for native English speaking people in the teaching fields, and that more and more companies there are looking for English speaking people to work for them. So, I guess what I am trying to find out, is if there are people out there, especially ones from America, that have gone through the process. For example, did you go on a tourist or student visa, and found an opportunity that was too good to pass up, and decided to stay...and if so, how did you manage it? Did the company you work for have to vouch for you, or assist you with any of the new visa work? Did you have to show proof of residency? Are you allowed to rent an apartment, not being a citizen?
As to the problems different countries may have, well all I can say is that there is good and bad everywhere, and perhaps for my personal reasons, I may find Russia to my liking, and offer me opportunities that are unique for me.
I guess what I am asking for is perhaps simplistic, but if there is any such thing as a "step-by-step" guide on how to move to Russia, then that is what I am looking for. Thanks everyone!