1 GB 667 MHz DDR2 SDRAM
Although it appears the rest of your hardware can handle up to Mountain Lion 10.8, you will need more RAM. Lion 10.7 introduced the min RAM needed of 2GB and more is better.
Do "About this Mac" and, in the resulting window, click the "More Info..." button to launch System Profiler. Profiler's first screen looks like this:
except yours with say "iMac" instead of "MacBook Pro" in the example. Please post the info following "Model Identifier" (the second line) and we can accurately advise what RAM upgrade path will work for you.
There are several 2.4Ghz iMac Core 2 Duo models and not all take the same RAM nor do they have the same max RAM capacity. That Model code will let us preciesly identify your model and make well-targeted suggestions.
Also if you give us a rough idea of where you are located geographically, we may be able to point you to RAM vendors that have high-quality yet affordable RAM for Macs.
This is the information from my iMac.
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: 1 GB
Bus Speed: 800 MHz
Boot ROM Version: IM71.007A.B03
SMC Version (system): 1.21f4