Home location on CNC Lathe

Hi all, I have done lots of Google search, but are still confused about where the home position on a CNC Lathe should be? As the machine needs to home after e.g. a power out and potentially tools are mounted and some metal can be in the chuck, I would assume the safest place for the home location would be as far away from the chuck as possible, i.e. max +Z and max +Z as shown in that lathe image found on linuxcnc.org.

Obviously that means long travel distance to get to home and back from home to work, but it should be safe.
Does that make sense ? Or what is the recommendation ?

Yes, the typical position for home is Max Z Max X. My Hitachi Seiki lathe homes X then Z, I believe this is to avoid a potential crash with the center, but assumes you didn't leave a boring bar in the bore of the work when you powered down.

Thanks, one more follow up question:
Would this than be location 0,0 or how should I set coordinates ?

I haven't had the lathe in G53 for a while, but as I recall, it's X8.8 Z12.5 in G53, which puts 0,0 at the center of rotation and near the chuck (But not actually at the chuck face). I would definitely have X 0 at the center of rotation.

If I could add to (or perhaps confuse) @B.Reilly01's excellent suggestions... the X-home also depends on the lathe hardware.

X0 at center of rotation... in relation to what feature on the X axis?

Consider three different lathes: flatbed with tool post, turret (slant or flat), and gang-tool.

On my slant turret lathe, X0 is when my turret's tool-holder bores (it's a VDI) are concentric with the spindle.  Simple and easy to remember & indicate.

On a flat-bed lathe with a tool post... what reference feature/surface on the X-axis will never change?  I would argue that the face of the post (if there is a face) would make the most sense.  But if you've got a tool post with no ground surface or edge, then maybe the end of a standard tool holder would be suitable.

Radial tools would all have a positive X-offset, but some axial tools (boring bars) may have a negative offset.  Not ideal for quickly verifying tool offsets are appropriate for a job.  Maybe use an axial tool holder with a collet/drill chuck, and when that's concentric with the spindle - X0.

For a gang-tool lathe the X0 point is even more slippery.  You can have front tools, back tools, M3 tools, and M4 tools.  Which one is X0?  Is there a tool that never moves (think parting blade near the end of travel)?  On the gang lathe I'm building it's easy - when the sub-spindle is concentric with the main spindle, that's G53 X0.  But I don't think there are many gang-tool lathes with subs around.

Point of the above jabbering is that G53 Z0 is pretty obvious, but X0 needs some thought.  What makes the most sense to the user, based on the hardware and intended programming method/style?

The following makes most sense to me:

Home is max X, max Z (the furthest position from the spindle nose)

Home is 0,0. This means if working in g53 (machine coordinates), it's obvious what is going on. To me G0 G53 Z 0 should go to a safe position, and works the same on lathe / router / mill.

As pointed out, different tools have different X offsets / positions, so there is no fixed X0 centre of rotation.

G54 (work coordinates) are different. Usually tool tip will be at centre of rotation with G54 X0 (with appropriate tool offset)