Q: I run OS X 10.7.4 what OS is best to upgrade to?

Assuming your Mac can upgrade beyond Lion 10.7, then you have 2 choices.  Mountain Lion 10.8 or El Capitan 10.11.

Mavericks 10.9 and Yosemite 10.10 are no longer generally available.  UNLESS you have previously downloaded Mavericks and/or Yosemite, then they would be listed in your App Store -> Purchases tab.

You can go to the on-line Apple Store and pay for Mountain Lion 10.8.

OS X Mountain Lion system requirements - Apple Support (upgrade requirements)

http://www.apple.com/shop/product/D6377Z/A/os-x-mountain-lion (order via this link)

You will get a redemption code to allow you to down load it.

Or you can download the free El Capitan 10.11

OS X El Capitan - Technical Specifications (upgrade requirements)

Apple has historically supported the 3 most recent versions of OS X, so that would be Mavericks, Yosemite and El Capitan.  Older versions no longer get security updates.

If you with to test El Capitan, you could see if you can create a 20GB to 30GB partition on your Mac and install El Capitan in the partition and test it out.  I understand that a Macbook Air does not have much storage, but that is the best way to see if El Capitan will be a good fit for you.

OS X Lion, junk, the version that should have been Mountain Lion.

OS X Mountain Lion, costs $20, and is not as good as El Capitan

OS X Mavericks and Yosemite, free but only available if you bought them in the year of their introduction.

OS X El Capitan, free.

If you have the first introductory model of the MacBook Air, then you're limited to OS X Lion, end of story. But, you should at least update it to 10.7.5.