goddam page timed out while i was typing my first reply. right. short version.
060. preferable to have 1E41J mask revision chip, as generally regarded to be able to go upto 100Mhz. but you will not get that far.
ram. the faster the better. 60ns or faster. usually noted by having -60 or -6 on the end of the number on the top of the chip. slow ram = bad.
sync/async. the 50Mhz clock maybe driving your system board's 25Mhz core clock, so unless to can de-couple it (run it asyncronously) from the system clock, you'll be pushing your system board faster, and this can be considered a "bad thing"(tm). you'll probably be pushing your video timing out of sync by force feeding a 30/33Mhz clock to the system from a 60/66Mhz cpu clock - and not even boot.
cooling. not just the cpu will be getting hotter. but the cpu interface logic, bus buffers and controllers, memory logic, and power regulators. check from other components gettting more toasty the faster you push the system.
power. some old circa 1990 AT PSU from the bargin bin at a closing down sale of your local PC highstreet shop probably isn't going to cut the mustard. faster=more power consumed, as well as more heat generated. that PSU may be rated to 350 watts, but it if starts putting out wobbly voltages the harder its working, then the tighter tollerances of running faster will be all for nought.
the quickpac board itself. if iirc, is quite big. you may have problems with the timing going across such a big beast keeping all in sync. but good design and manufacturing may pull a rabbit out of the hat in this regard. plus it can use EDO ram properly, so thats an immediate 10-20% ram bandwidth boost.
hope it works out, as even a modest increase from 50 to 66Mhz on an 060 can give a third increase in power. much beyond this, and you may find your RAM to be your limiting component. thats why the PC world went to 64bit 66-100Mhz SDram Dimms from 32bit FPM/EDO simms, as 66Mhz was about the break point.
