Machione coords zero should be with the tool fully negative in X and Y and fully positive in Z.So that would normally be lower left and fully up.
If you press RefAll and you dont have home switches then you will set Machine Zero at the position your table is presently, you dont really want to do that especially if you wish to use soft limits.
Normally you will just zero the work coordinates by pressing the zero buttons at each DRO.
If your axis are running backwards then that is the first thing to sort, in fact it sounds like you may have the axis wrong in as far as you say Y moves left to right and X front to back, that is incorrect, it should be the other way. You can of course have it that way if you wish, its up to you but the toolpath view in Mach will always be rotated compared to your table and will likely cause confusion, best sticking to convention I would say.
So to summarise, X moves left/right and Y Front/Back. X moving the tool to the left is going negative, Y moving tool to front is negative. Z moving up is positive.
Hood