How long is a piece of string, the answer re-glue is much the same.
If open segments with room to move then anything from PVA upwards that bonds well.
If close coupled then you need to consider wood movement more with air moisture changes, PVA and similar will still hold but you may 'feel' the join after a while as the glue creeps to accommodate wood movement.
I personally use Cascamite as it does not creep so joints stay put, but wood moisture balance has to be better controlled if disasters are to be avoided with wood splitting rather than joint moving.
Experimenting is the best learning curve but can lead to frustration and disappointment.
You will see reference to grain orientation causing failures, that's never been my experience, wood moisture content has always been at the root of any of my problems.
Make sure your wood is drier than any expected home humidity level before final sizing and glue up, that way wood and glue joint will always be in compression one completed.
