If you understand bucklers they do not provide any less defense in melee than a rotella (round shield) or heater (most commonly depicted knight shield like the one used in Zelda). They actual provide about the same melee defense but with better visibility which is why they are preferred for duels. Bucklers are not good for ranged defense however.
You could honestly do small shield = buckler, Standard shield = rotella/heater/wrankel, Tall shield = tower/kite/oval/celtic/coffin etc.
Your melee damage is backwards. Bucklers are extremely good a punching and intended for it. Heater shields have a special variant where the strapping is vertical in stead of horizontal placing the handle at the point specifically for punching.
As you also depicted with weight requirements most standard and heavy shields are not good as melee weapons because they are too slow for strikes. They are useful for body checks but that is basically the special action "shove" and you can body check without a shield it just gives you defense.
Daggers are also very good for melee defense but again suck for ranged defense.
I would suggest
Off Hand Sparing Dagger +2AC vs melee attacks, 1d4 damage, light, finesse
Buckler/Punch Shield +2 AC vs melee attacks, 1d6 damage, light
Standard shield (rotella/heater) +2AC vs ranged and melee, 1d4 damage as an improvised weapon.
Tall shield (tower/kite/oval/celtic/coffin) +4AC vs ranged and melee, requires str 13, advantage on dex saves hiding behind the shield.
I am not sure why you would have a disadvantage to stealth for a shield. They are not noisy and black or brown tower shield would still be harder to see than a brightly painted or metallic buckler. That would be up to the owner. Also, if your carrying a heavy shield you likely have heavy armor anyway so its redundant.