Replacing my old fan, avoiding mistakes

When I built my first computer, I made the mistake of skimping on the fan a bit, with the result that I am stuck with something that is very loud and doesn’t even do its job properly. I would like to replace it with something better. I have looked around and the ARCTIC Accelero Twin Turbo II seems like a good option. Is there anything I should be aware of? Are there any compatibility problems? Is it worth the expense in a fairly old computer?
