I'm concerned about these new Weapon Attack (and Magic Attack) values. I don't like them on a visceral level. Okay, I'll be more specific. They don't feel like D&D and they make me think that the design team is losing touch with what D&D should feel like.
The lead designers have talked a lot about their 'bounded accuracy' system, which sounds good on paper (to keep monsters versus chatacters relevant longer), but starting classes off with a +2 or +3 attack values strikes me as more than a little arbitrary, counterintuitive, and plain ole screwy, especially considering how generic weapons have become in the play-test. Right now, damage is the ONLY mechanical difference separating weapons. How freaking boring is that? There's no decision. You take the highest damaging weapon. Done. Picking weapons used to be more enjoyable than that.
Weapon Properties by Group
Axe: Can reroll the minimum damage result once per attack and add amounts together.
Bow: Can impose disadvantage to opponent rolls on a critical hit until the end of their next turn.
Crossbow: Gain advantage on attacks against armoured opponents.
Dagger: Can add Strength and Dexterity modifier to melee damage while keeping one hand empty.
Flail: Can trip opponents prone on a critical hit, or by taking disadvantage on an attack without dealing damage.
Hammer: Can stun opponents on a critical hit until the end of their next turn.
Mace: Can add Strength and Dexterity modifier to melee damage against armoured opponents.
Pick: Can restrain opponents on a critical hit until the end of their next turn.
Shield: Can push opponents back 5 feet on a critical hit, or by taking disadvantage on an attack without dealing damage.
Sling: Can knock opponents unconscious on a critical hit until the end of their next turn.
Spear: Gain 10 feet normal range (40 feet maximum range) by taking disadvantage on any attack using the extra range.
Staff: Gain reach by taking disadvantage on any attack using the extra 5 feet.
Sword: Can disengage or coup de grace as a move instead of an action.
Unarmed: Can make two unarmed attacks or while keeping both hands empty, both of which deal half damage. Can do the same if one or both hands are wielding one-handed improvised weapons.
Whip: Can disarm opponents wielding one-handed weapons on a critical hit, or by taking disadvantage on an attack without dealing damage.
I like how the original poster designed these Weapon Properties by Group, creating thematically appropriate effects for different weapons. That's certainly one place to build differences between weapons, but why not 'borrow' a little from 4th edition as well (it wasn't all bad) and reincorporate proficiency bonuses. That would kill two birds with one stone. Not only would weapons feel 'that much more' unique (moving beyond their bare damage values), but it could also eliminate those seemingly arbitrary mathematical (accuracy bounded) +2 and +3 attack values granted to classes at 1st level.
For that matter, different holy symbols and implements could also have proficiency bonuses, so long as they also come with their own Implement Properties by Group as well. Nothing too specific. Just broad differences, similar to what the original poster created with weapons.