Have you been directed to the 4e discord server for utility wear? like Character Builders and VTT support tools?
Agree here as 4e player option books are not good reads per se. They are reference manuals and you don't really need them if you have access to the character builder and other tools.
So physical copy wise I would start with:
PH, PH2 just so you get how classes are laid out. You can get the other class features and class powers from the characer builder/databases
Neverwinter Campaign -- so you can see how themes can be incorporated and the flexibility of 4e to squeeze a full campiagn into 1-10 levels
MV, Threats of Nentir, and Dark Sun Creature Catalouge to inspire good monster building (the rest can be gotten from the database)
If you want more:
DMG, DMG 2 - two of the best DMGs
especially the later lore books were a huge strength of 4e -- planes above, planes below, underdark were particularly good