In the general case, you want the origin to be at the centroid of the part. That makes the placement coordinate used in manufacturing and the part origin the same thing (usually).
However, in this case, I'd pick the origin more for benefit when placing the part outline on the board during board design. This kind of part needs to placed relative to the board edge, so I'd put the Y of the origin (using the orientation in your drawing) at wherever the edge of the board is supposed to be relative to the part. I'd then center the X of the origin.
Yes you can move a part around so that it is lined up properly with the board edge regardless of where its origin is, but that's not so easy. Most CAD packages will snap coordinates to some grid, which may have to be disabled if the offset from the board edge to the origin is not a nice multiple of a reasonable grid resolution. Also, you'd still be left eyeballing the placement. With the origin at the board edge and centered around the part in the other dimension, it's much easier to type in the placement coordinate and put the connector exactly where it's supposed to be.
Another thing I'd do is add some silksrcreen or at least something in a documentation layer that indicates the board edge. Don't assume you'll remember the details of this particular connector when you lay out the board, or lay out a different board a year later.
For example, here is a connector where I've done as described above:
The dashed line indicates where the board edge should be. This connector actually hooks around the edge of the board a bit for better mechanical strength. The blue rectangles are in the bottom keepout layer to indicate nothing should be placed there because the connector is taking that space.
The text "Board edge" is in the top documentation layer, and is only for use in placement. It indicates the meaning of the dashed line, which is easily forgotten months later after the connector package was created, or for other people that never knew this in the first place.
Note also the arrow indicating the direction the mating connector will be plugged in. This may seem obvious given the pads at the opposite end of the connector and the board edge, but it can be confusing on some connectors. I generally add this when the mating connector comes in sideways. Long ago I once placed a RS-232 connector the wrong way because the placement of the pads alone gave the opposite impression of which way the mating connector came in. Since then I've added arrow to sideways-mating connectors and haven't made that mistake again.
The origin of this connector is at the board edge in the middle, right where the arrow crosses the dashed line.