re: Why should the U.S. be an enemy of modern day Russia?

Well there are some major institutions like NATO and the EU which were developed as a bulwark against then-Soviet aggression. Combine that with the insistence of both institutions to move eastward, taking in former Warsaw Pact countries, which is deeply opposed by Russia, which forms the basis of the disagreement at the moment. Many of the Warsaw Pact countries are deeply distrustful of Russia, and the eagerness with which they want to join protective blocks is a sign of how seriously they view the Russians as a threat.

Russia is naturally outflanked, and thus has moved to different regions in order to open access to markets, and develop relationships with key countries. Russia's key moves, outside of gaining a stable, warm water port (perhaps in Syria) is to prevent itself being outflanked. It's relationship with Iran can be explained in this regard. The key in this is what happens to Turkey in the next 30 years. If somehow Russia and Turkey can develop a closer relationship, undermining both NATO and Turkey's aspirations to the EU (which is effectively dead at the moment), it could gain access to the Mediterranean and upset the West a great deal.

In general, Russia and the US will be diametrically opposed about most things, but that is to be expected. Whether they become an enemy on the scale of the Soviet Union is another matter. But the Russians themselves feel very hemmed in, and will probably use diplomacy and then force to break out if they feel the need to.