I have an opportunity to purchase a rarely used Canon Speedlite 430EX flash. I admit I know next to nothing about flashes but want to learn the basics with this one. I understand that this is an older unit and that a Canon flash should be compatible with lenses and body. I have a "newer" 60D body and Canon lenses. Will there be any compatibility issues?
No. On the 430EX product page it says:
Compatible Cameras: All Canon EOS cameras...
Compatibility between Speedlites and bodies is very good within the Canon world. You don't always get 100% of all features, but the reason for this is generally obvious. For example, older bodies cannot program the radio trigger in the new 600EX-RT from within the camera's menus. But, you can program the optical trigger from the 5D Mk II menus. Further, it works as a normal on-camera flash on any EOS body, and it will work as a radio trigger if you set the triggering up using the on-flash controls.
The other direction — newer body, older Speedlite — tends to work without fuss, too. I've used an ancient 380EX on my 5D Mk II several times, for example. If you go with an old enough flash, like an EZ series, you will lose out on body features like E-TTL, but that should also be unsurprising.