Agree on the skill system - it seems to broad. I think I would change History to Lore, and then have some sort of way to specialize in a subset of a skill. The broad skills would still be useful to everyone, but true specialists could stand out (for example, a sage specializing in Lore (History) versus a wizard's general Lore skill). I think I would add Melee and Ranged as a skill (with the ability for martials to get specialization and/or expertise), and have spellcasters use Arcana, Religion or Nature for their spellcasting attack rolls (and maybe saves?).
I would carry over subclasses, but certainly would tweak them here or there. Redo the monk class from the ground up, add in a psionic (& possibly a psion/martial) class and a fighter/mage base class.
For me, the big thing would be Cantrips. I want the casters to keep some general effects and combat spells, but get rid of the ability to infinitely spam them (though likely to move Eldritch Blast to a class ability and not a cantrip, but still give some sort of usage limit). Guidance abuse needs to go, for sure.