The case of Russia in the Middle East is very simple, because the only thing that Russia wants is that the Middle East does not mess with the Russian sales in Europe. However it is very difficult for Russia to make friends in the Middle East, because contrary to the US, China and Europe, she is not an importer of oil and natural gas. Russia is an exporter and a natural competitor of the rich in oil and natural gas countries of the region.
It is not a coincidence that the oldest Russian ally in the region is Syria, a country poor in oil and natural gas, at least by the standards of the Middle East. As you can read in the following CNN article, titled “The Moscow-Damascus alliance: A tangled tale”, 2012, Syria has been a Russian ally since the Soviet Era and the 50s.
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Many observers point to Moscow's close ties with Damascus going back to the 1950s as a reason for Russia now acting to defend the alAssad regime in Syria against its many internal and external opponents.
http://www.cnn.com/2012/02/09/opinion/russia-syria-relations/
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Iran and Iraq are two of the richest countries in the world in terms of oil and natural gas reserves, and they are Russia's natural competitors. However they have been very close to Russia, due to their rivalry with the West. Their rivalry with the West, with the economic sanctions that this rivalry implied, prevented Western multinationals from entering and investing in the Iranian and Iraqi energy markets, and therefore the production in Iran and Iraq could not reach the levels reached by Saudi Arabia, Qatar, Kuwait, and UAE.
Moreover, very often these countries could not export to Europe due to economic sanctions. Therefore they were not Russia's major competitors. In addition Iran and Iraq were very good customers of the Russian armament industry. Russia is also developing the Iranian nuclear program. Contrary to US, China and Europe, which are all importers of oil and natural gas, Russia is a major exporter, and therefore tensions in the region are very good for her, because they drive oil and natural gas prices upwards. While high oil and natural gas prices make governments in USA, Europe and China unpopular, they increase the revenues of the Russian government, and allow it to increase public spending, which is always very popular with the electorate.
But if Iran and Iraq manage to work things out with the West, they will no longer need Russia, and they will no longer have a motive to be aligned with her. These countries only need Russia as long as they are in bad terms with the West. The problem for the West is that it is very difficult to be in good terms with all the rich in oil and natural gas countries of the region, because these countries are very hostile towards each other, in a non-stop fight about who is going to better promote his oil and natural gas.
However it is still correct to say that it is much easier for USA, China and EU, than it is for Russia, to make friends in the region. The United States, even though they increased significantly their oil and natural gas production, they are still one of the world's largest oil importers. Actually the US was the largest oil importer until 2013, when it became second to China, as you can read in the following article of the Energy Information Administration, titled “China is now the world's largest net importer of petroleum and other liquid fuels” , March 2014.
http://www.eia.gov/todayinenergy/detail.cfm?id=15531
The Middle East always welcomes large oil and natural gas importers, as long as they do their shopping in the region of course. Therefore China, the US and Europe will always choose their allies, and Russia will only be able to pick what is left in order to make alliances.