If you own one Amiga model (A3000, A1200, A4000) pumped up with enough memory you can even find some solutions to load and remap the whole Kickstart in fast memory and go.
Regarding compatibility:
Obviously AmigaOS 3.0 and AOS 3.1 and superior versions are best served by Kickstart rev.3.0 and rev.3.1.
Kickstart rev.3.1 it is the last one and differs from rev.3.0 by some minor changes and details.
Either AmigaOS versions v.3.0 and AOS v.3.1 run fine on both Kickstart versions.