I moved here to Indiana from Russia a couple of months ago, but I've been to the US before as an exchange student. From my experience, once you've crossed the border, you become an American an as welcome here as any other immigrant or as a native American. People will sometimes ask you where you're from, of course, but it will be just a question of curiosity, they won't treat you in some special way no matter where you are from.
One thing to consider: you really need a good spoken English to feel incredible here. I consider myself an excellent speaker (for a foreigner), and yet sometimes I have some difficulties expressing my thoughts, although I understand 99% of what people here say. Without good language, you really are going to feel out of place: people won't treat you any differently, but you yourself will feel a little bit alien, like I did in Japan when I lived there knowing only a few Japanese words.
Another thing: once you've moved in, you want to change your behavioral pattern from Russian to American, just to better fit in. In Russia, for example, smiling at strangers is almost a taboo, people will think you mad if you do that - but here it is completely normal, so if you will walk here with that sad expression they typically walk in Moscow, people will think that something tragic happened in your life, or you are just in a very bad mood. It is not just smiles, of course, you want to learn all the differences between cultures.
All in all, the USA is an amazing country, it is the most welcoming to immigrants country I've ever been to, together with Canada and Australia. People here are great and friendly, career opportunities are limitless (provided you are willing to work hard), life quality is very high. You will definitely like it here!