Dosbox is somewhat slower than pc-task, so Id be surprised if you reached even "high end" 286 speed even on the fastest of '060's. Remember that even sam boards struggle to perform at low-mid spec 386 speed.
Running my 68k/os3.x Dosbox under amithlon on a core2duo @ 3.86ghz gives roughly mid spec 486 speed, so being that my amithlon box is probably 100x as fast as the fastest '060.......
Absolutely no chance of running running Win98 or ME. In theory 98 can be installed, but it'll be slow as all heck. ME simply wont work. The only amiga-oid system capable of running 98 at a usable speed is x86 aros both because the speed of the hardware its running on, and because of the Dosbox code paths (and maturity of those code paths) avaiable to it.