Help to understand axes directions

Hello Mates, 
i'm having trouble understanding the proper axes directions between machine vs tool directions.
This is the first CNC I'm commissioning.

When the table is moving to the left, closer to the lathe the X should increment?
When the machine is moving toward the light blue wall the Y should increment?
When the table is moving down, closer to the floor, the Z should increment?

I'm setting my home positions and to order to:
1st: Z all the way down, nearest to the floor at value 0.0
2nd: X all the way to the left, nearest the lathe at value 0.0
3rd: Y all the way back, nearest to the wall at value 0.0

Greetings!
 

Does this help?
linuxcnc.org/docs/stable/html/user/user-...chine-configurations

Edit:
Homing should be
Z ok
X oposite
Y oposite
Although with LinuxCNC you can make it home anyway you like and still have 0 at the bottom left side.

Hi,

it did not, I stared a lot over the milling machine picture and just got more confused, I'm missing some concepts

When the table is moving to the left, closer to the lathe the X should increment?
When the machine is moving toward the light blue wall the Y should increment?
When the table is moving down, closer to the floor, the Z should increment?

That is correct.

I'm setting my home positions and to order to:
1st: Z all the way down, nearest to the floor at value 0.0
2nd: X all the way to the left, nearest the lathe at value 0.0
3rd: Y all the way back, nearest to the wall at value 0.0

The home position is up to you. There is nothing wrong the way you have it.

Im still confused, Mr Aciera is says the first post is correct, Mr Tommy says X and Y are opposite , which is correct or what should I set?