First thing I'd do is...
1. Insert the10.6 Mac OS X Install disc, then restart the computer while holding the C key.
2. When your computer finishes starting up from the disc, choose Disk Utility from the Installer menu at the top of the screen. (In Mac OS X 10.4 or later, you must select your language first.)
Important: Do not click Continue in the first screen of the Installer. If you do, you must restart from the disc again to access Disk Utility.
3. Click the First Aid tab.
4. Select your Mac OS X volume.
5. Click Repair. Disk Utility checks and repairs the disk.
Make sure you have at least 30 GB of free space on the drive.
10.6 by default does what we used to call an Archive and Install, so all should be good.
After Install update to 10.6.8
Buy Lion online.
PS. You may be very disappointed with either OS with only 2 GB of RAM, at how soon things slow down.
10.5 needs twice as much as 10.4, 10.6 needs twice as much as 10.5, 10.7 needs twice as much as 10.6
Here's mine & I often run out of Memory & get real slowdowns...
Model Name: iMac
Model Identifier: iMac7,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.4 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 4 MB
Memory: 6 GB
Bus Speed: 800 MHz
Boot ROM Version: IM71.007A.B03
SMC Version (system): 1.21f4