It seems that if you select a race that starts with medium or heavy armor proficiency, you can actually wear chain, plate, etc, as a level 1 Wizard/Warlock/etc. Likewise, you could also theoretically pick up the armor proficiencies during feats every 4 levels (right?)
You can cast while wearing armor if and only if you are proficient with the corresponding armor type, no matter the source of said proficiency. That said, I'm not sure if casters are able to (or should) pick up armor proficiencies as feats on level-up.
Are there any drawbacks or penalties to casting spells or wearing heavy armor as a wizard? In my initial testing it does not appear to be. That seems to make playing something like a Githyanki or Dwarf a huge advantage, as your INT can still get almost as high but you can walk around like a tank. In fact, could you use a shield as well?
There are no drawbacks or penalties to casting while in armor, provided you are proficient. You can use a shield and cast if your other hand is free, i.e. you are not carrying a weapon. If you are carrying a weapon AND a shield, you cannot cast spells that have a somatic component unless you have the War Caster feat.
