Re: standar for movements?

Yes there are standards and you do want to imagine the tool moving, not
the table. This makes it easier to visualize.
The Z axis is usually the axis parallel to the machine spindle axis.
Machinerys Handbook shows the different axis designations for different
machine types. It's in the section on numerical control
For vertical milling machines, (ref the tool not the table), looking at
the machine from the front.
Pos Z is up
Pos Y is away from operator
Pos X is to the right.

when you have your machine set up right, the table will move the
opposite way of the jog keys. this is why it's best to stop thinking
of the machine in terms of table movement.