How do I just get my computer updated so I am not constantly chasing the newer version of one thing that affects everything else on the computer?
Switch to Windows 7 PC, ten years of no changes and no upgrade games.
Windows 7 Pro+ even runs XP programs.
Seriously, run Software Update under the Apple menu, it will bring you up to 10.6.8 and Safari 5.7.1, iTunes 11.
However Safari 6 is only on OS X 10.7 and 10.8, so since because of that, you should switch to Chrome or Firefox for 10.6.8
Your machine is likely too old to run 10.8, even if it can, it likely will be slow and require more RAM etc.