External hard drives just need to be formatted properly for the type of computer you have. Some manufacturers, like Western Digital and LaCie, may include special backup software that is only compatible with certain OS's, but the drive itself works just fine.
Make sure you get an external hard drive that is at LEAST as big as your internal drive.
You may want to check out what Other World Computing has to offer. Their drives are compatible with Macs running at least 10.0.x (so your current computer definitely qualifies) and they're a very reputable company.
Once you have an external hard drive, I suggest downloading Carbon Copy Cloner to do a bootable backup of your MacBook's hard drive. With a bootable backup available to you, you have nothing to worry about if your upgrade doesn't go well - you can wipe the internal drive and clone back all your data very easily.
I hope that helps you a bit - if you have questions, please do ask!
~Lyssa