HI & a warm welcome! 🙂
So we know more about it...
At the Apple Icon at top left>About this Mac, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...
Hardware Overview:
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
10.5 can be found, but 10.6 is far cheaper.
Leopard requirements/10.5.x...
* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor
minimum system requirements
* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)
* DVD drive for installation
* 9GB of available disk space (I say 30GB at least)
Classic/OS9 Apps no longer supported.
Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...
http://www.ebay.com/sch/i.html?_nkw=mac+os+x+leopard+retail+10.5
Snow Leopard/10.6.x Requirements...
General requirements
* Mac computer with an Intel processor
* 1GB of memory (I say 4GB at least, more if you can afford it)
* 5GB of available disk space (I say 30GB at least)
* DVD drive for installation
* Some features require a compatible Internet service provider; fees may apply.
* Some features require Apple’s MobileMe service; fees and terms apply.
Which apps work with Mac OS X 10.6?...
http://snowleopard.wikidot.com/
It's been pulled from the online store & Apple Stores, so you have to call Apple to buy it, last I heard.
Buy Snow Leopard > http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
Call Apple Sales...in the US: 1-800-MY-APPLE. Or Support... 1-800-275-2273
Other countries...
http://support.apple.com/kb/HE57