64 bit/32 bit Linux runs on any x86_64 processor, either AMD or Intel
That is true, but there is a difference between AMD and Intel. A distro that has an .iso labeled for AMD and another normal one, will have differences in them. The differences is in compilations and Flags and all that good S**T. In the past there was a lot of differences between the processors, But as they grow more alike, there is less difference between the software compliled on each system.
If the Distro of your choice has both amd and normal isos, you'd be adviced to choice the one correct for your hardware.
You said you researching 32bit via 64bit!
The software developement moves at a very fast pace. But about 1 year ago, my dad bought a 64 bit system to do vidio editing, at that time. Even though the kernel and most the 64bit distro was 64bit, the software he needed was 32 bit still, and so he had 32bit software doing his editing still. True he had a fast a machine, but as of 1 year ago, there was little advantage for him to have 64 bit. Each persons needs determine wither or not it's worth it.