Your best bet for a 10.5 era machine is to get to 10.6.8 via the 10.6.3 white retail disk (call Apple via phone to order) and stick with 10.6.8.
10.7 or 10.8 will make it crawl, introduces radicial UI changes and cant' run your older PPC based software and hardware drivers.
You should do this with a fresh install method, backup your files off the machine first to a storage drive.
Then follow these instructions for a complete drive Security Zero Erase and install of 10.6.3
iLife from the 10.5 disks can be extracted with Pacifist from CharlesSoft and then updated via Software Update.
If you upgrade 10.6.3 over 10.5, then you will have a much slower machine and wind up having to do a fresh install anyway.
10.6 is faster than 10.5 with updated video drivers and removing of PPC code your not using on Intel processors.
10.7 and 10.8 are slower on the same hardware, more for the faster SSD's than hard drives.
Also first chance you get, make disk copies of the 10.6.3 disk, you will need it as eventually Apple will stop selling it.
Run 10.6.8 until the wheels fall off that machine, Apple is still supporting it as over 50% of it's users are still on it.
Buy a new machine with 10.9 or whatever and new software later on, when Apple has stopped all these annual UI changes, restrictions and whatever they are doing.
Keep in mind that Microsoft will support Windows 7 until 2020.
You might want to upgrade the boot hard drive (7,200 RPM is good for older machines with slower SATA 1 or 2) and add more RAM before reinstalling OS X