In general, the Windows version of the UAE Amiga emulation (WinUAE) requires an Intel Pentium or 100% compatible CPU (e.g. Celeron, Xeon, Itanium).
The NexGen "586" CPU is not Pentium-compatible (it is a fast 386 clone).
Some versions of WinUAE have a special option for Cyrix CPUs. Please refer to the specific notes about the Cyrix CPUs in the Installation section of the Amiga Forever 2.0 documentation. This does not apply to newer versions of Amiga Forever, in which WinUAE does not have this option (it is not required any more).
AMD CPUs are not known to require any particular settings.