Im think of trying an Achromat on my LP-12. Would I be better off going with the 3mm than the 5mm?
this is purely my opinion/logic - if you have enough spindle height to use the 5mm, go with it, otherwise use the 3mm. If you're not using a clamp (which you shouldn't really need with the achromat) then spindle hight probably isn't an issue.

Also - if you go to the Funk Firm website and send them an email you may get their (more authoritative) guidance.
I like the Boston Mat better...
Well, since the stock felt mat is pretty thin and I'm working with a suspended TT, I ended up ordering the 3mm Achromat. Less tinkering. I have a nonefelt/speed mat on my other turntable that I'll be able to swap for some comparison.