Yes, that is Snow Leopard. Yes, you can purchase and download Mountain Lion from the App Store. If you are concerned about your files and pictures, then you should make a backup before upgrading. Go buy an external drive on which to put the backup. Or see:
Basic Backup
For some people Time Machine will be more than adequate. Time Machine is part of OS X. There are two components:
1. A Time Machine preferences panel as part of System Preferences;
2. A Time Machine application located in the Applications folder. It is
used to manage backups and to restore backups. Time Machine
requires a backup drive that is at least twice the capacity of the
drive being backed up.
Alternatively, get an external drive at least equal in size to the internal hard drive and make (and maintain) a bootable clone/backup. You can make a bootable clone using the Restore option of Disk Utility. You can also make and maintain clones with good backup software. My personal recommendations are (order is not significant):
1. Carbon Copy Cloner
2. Get Backup
3. Deja Vu
4. SuperDuper!
5. Synk Pro
6. Tri-Backup
Visit The XLab FAQs and read the FAQ on backup and restore. Also read How to Back Up and Restore Your Files. For help with using Time Machine visit Pondini's Time Machine FAQ for help with all things Time Machine.
Although you can buy a complete external drive system, you can also put one together if you are so inclined. It's relatively easy and only requires a Phillips head screwdriver (typically.) You can purchase hard drives separately. This gives you an opportunity to shop for the best prices on a hard drive of your choice. Reliable brands include Seagate, Hitachi, Western Digital, Toshiba, and Fujitsu. You can find reviews and benchmarks on many drives at Storage Review.
Enclosures for FireWire and USB are readily available. You can find only FireWire enclosures, only USB enclosures, and enclosures that feature multiple ports. I would stress getting enclosures that use the Oxford chipsets especially for Firewire drives (911, 921, 922, for example.) You can find enclosures at places such as;
1. Cool Drives
2. OWC
3. WiebeTech
4. Firewire Direct
5. California Drives
6. NewEgg
All you need do is remove a case cover, mount the hard drive in the enclosure and connect the cables, then re-attach the case cover. Usually the only tool required is a small or medium Phillips screwdriver.
Upgrading to Mountain Lion
To upgrade to Mountain Lion you must have Snow Leopard 10.6.8 or Lion installed. Purchase and download Mountain Lion from the App Store. Sign in using your Apple ID. Mountain Lion is $19.99 plus tax. 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.
For a complete How-To introduction from Apple see Upgrade to OS X Mountain Lion.
