IMO, yes. It should take a Minor action to draw or put away a weapon or shield. Dropping one should be a free action.
And a free action if it's combined with a move action and your BAB is +1 or higher. (Can you tell I DM and like 3.5e?

IMO, yes. It should take a Minor action to draw or put away a weapon or shield. Dropping one should be a free action.
And a free action if it's combined with a move action and your BAB is +1 or higher. (Can you tell I DM and like 3.5e?)
I think I would prefer to see the action cost based on size of the weapon. Drawing a dagger or dart? Free action. Drawing a longsword, or readying a mace? Move action.
This would allow you to get rid of minor actions (at least for purposes of drawing weapons), and would provide an interesting contextual reason for a fighter (fighter here meaning "one who fights" not just the class) to carry, and occasionally use a small light weapon.
Something I really want to see from 5e...less emphasis on specialization. I want a fighter to begin a fight throwing an axe, then drawing a broadsword. At some point it's knocked from his hand, and he grabs a knife, wrestling with an orc as he stabs him in the chest.