According to Microsoft (that now owns Skype)
Skype no longer supports Mac OSX 10.5 (Leopard) and below.
So you have to upgrade your OS X to next version or higher.
For OS X 10.6–10.8 use Skype for Mac 6.15
For latest Skype you need minimum OS X Mavericks or latest Yosemite.
Going above 10.6 (Snow Leopard) it is highly recommended to do memory upgrade from now 2 GB to 4 GB.
Memory upgrade is not big challenge and it can be done by you.
It does involves opening the computer and replacing hardware.
My recommendation would be you go for the Snow Leopard (without memory upgrade) and give it a test run with Skype version downloaded from here:
What do you need and how to upgrade to Snow Leopard.
Once you are on Snow Leopard you can easily (for free) upgrade to Yosemite if you want to, and also get latest Skype, but it might be slow if you do not upgrade memory.