As everyone said, veneer last. I have never double veneered, imho it causes other issues with balance.
One other item to consider is the wood species. I also match the veneer glue color to the veneer. For darker wood (i.e. walnut) I use dark-tinted veneer glue; not only helps with hiding the difference in the substrate but also helps in case of bleed thru. I generally only veneer with darker wood or closed grain wood and have not had any issue (walnut, cherry, maple, anigre). For solid edging I usually have at least 12 mm (1/2") thick bands (thicker if there will be some profile routed later): Makes glue up much easier. A lipping planer followed by careful sanding for a flat panel is next. Some of the glue lines are due to the environment: Adding glue to MDF/solid edging will cause some minute differential swelling, I let the clue cure for at least one day before planing/final sanding. Also, both substartes should be acclimated before final sanding/veneering. I had one incident where I veneered an edgebanded panel while the AC in my shop was out for a couple of days: That panel showed gluelines a bit; likely due to the difference in moisture uptake/swelling of the 2 substartes followed by the drop in humidity after the AC worked again.
And lastly, pressure during veneering: Vacuum veneering is fail save since the pressure is limited to atmospheric pressure. But using clamps/cauls/hydaulic presses can exert much higher forces and can actually dent the material, if a excessive force runs over a glue line, then it will show.
hope that helps.
Bernhard