There are only two options for you. Mountain Lion or El Capitan.
Upgrading to Mountain Lion
To upgrade to Mountain Lion you must have Snow Leopard 10.6.8 or Lion installed. Purchase a redemption code at the Online Apple Store: OS X Mountain Lion. Mountain Lion is $19.99 plus tax. Use the code to redeem a download of Mountain Lion from the App Store. The file is quite large, over 4 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.
OS X Mountain Lion - System Requirements
Macs that can be upgraded to OS X Mountain Lion
1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later.
2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model
Identifier 5,1 or later.
3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later.
4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later.
5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later.
6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later.
7. Xserve (Early 2009) - Model Identifier 3,1 or later.
To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.
Are my applications compatible?
See App Compatibility Table - RoaringApps.
Upgrading to El Capitan
You can upgrade to El Capitan from Lion or directly from Snow Leopard. El Capitan can be downloaded from the Mac App Store for FREE.
Upgrading to El Capitan
To upgrade to El Capitan you must have Snow Leopard 10.6.8 or Lion installed. Download El Capitan from the App Store. Sign in using your Apple ID. El Capitan is free. The file is quite large, over 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.
Macs that can be upgraded to OS X El Capitan
1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later
2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later
3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later
4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later
5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later
6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later
7. Xserve (Early 2009) - Model Identifier 3,1 or later
To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.
Are my applications compatible?
See App Compatibility Table - RoaringApps