After we have cleared up by pm, what you disere is, I want you to tell here my humble opinion of upgrading your iMac 2006, 2 GB ram, to newer OS then Snow Leopard:
With system 10 7.0 began the real resource eating of OSX on the Core 2 Duo Mac platforms with ddr2 ram and the need of upgrading of ram. I had Lion running for some weeks on an MBP 4,1, 2,4 Ghz 4 GB ram, before it died the Nvidia gfx death.
In Comparison with running Snow Leopard on this device, it became under Lion less reactive, booting had lastet longer, and running it has therefore not made so much fun as before under Snow Leopard.
As far as I know, you should offically be able to upgrade the ram of your iMac to 3 GB, perhaps undocumented to 4 GB with limitations, depending on your nearer specs.
The biggest deal breaker of upgrading your iMac to Mavericks could be it´s gfx. This seems to be not compatible with the OpenGl 4.0, that is used by Mavericks, and it is not upgradeable, because of being soldered on the mainboard. (If I am right x1600 with 128 mb, neccessary X1600 256 mb)
In any case you have to hackintosh your iMac and format it MBR. I have collected some links for you worth to read:
(About upgrade 32-bit MacPro with upgradeable gfx)
The most important for you seems to be that one: (patched x1600 kexts available?)
If you search in google with arguments: unsupported mac Mavericks or unsupported mac Mountian Lion, you will find tons of matches, You should also do a search for patched kexts for your gfx.
My conclusion is the following:
If you have time and it makes fun for you to hackintosh your iMac you could try it with Mavericks, if you are able to find verified working patched gfx-kexts. You can also try to install Mountain Lion, if you can find out, if your gfx is working without patching or if patching is neccessary, then only, if it is verified working.
But as I have written before, I doubt, that using the system itself makes real fun. If you could get it working with Mavericks or Mountain Lion and you want to use it for more then fun, then you should think about trying to upgrade ram to 4 GB and a SSD harddrive with about 240 GB space.
In any case, if you try to hackintosh your iMac, you have to clone your partitions to an external Guid partitoned harddrive with CCC and keep them save. After installing Mav/ML you have just to clone them back and install chameleon on the clone to be afterwards able to boot the cloned system.
You can make your usb installer for Mavericks or Mountain Lion following this guide:
Please post here your results.