Should I look to add a planar contraint or corner constraint as soon as possible? It seems that if I add it later, it will either be rejected or it will warp the picture.

Hello,
 
You should add only constraints if you are sure of them, as they have a strong impact on the calibration engine.
Generally one corner constraint per "main" plane (Oxy, Oxz, Oyz) is sufficient.
Planar constraints should be set after a worldspace has been set (worldspace=coord system )
 
Note: Constraints are not necessary to get a calibration and they do not have and impact on the number of marker to place. BUT, they help generally to improve and fine tune a calibration, with better respect on real data.
 
Stef