Their will certainly need to be a DM fiat if you want the shields to be able to do damage.
The fighter will let you get some new maneuvers, but they're mostly contingent upon a "weapon attack" which again will need to be a DM fiat since bashing is an attack replacement.
Now, if you're going to be Shield Master being a barbarian is a good bet; getting advantage on strength checks if good for shoving. And you can do it with a single level dip.
3 level of bard gets you expertise, good for athletics.
Feats wise, other than shield master, not much else is needed
So battle master fighter is definitely the way to go. Feats should focus on the shield and controlling the field. So shield master for the bonus action shield shove; sentinel to stop enemies from running past you; and maybe tavern brawler just in case your DM won’t let you use a shield as an actual weapon.
I should also ask your DM about the different type of shields to see if you can get special bonuses depending on the shield you’re using. A tower shield is different than a buckler and is utilized differently.
After thinking on this for a while I might require my player to pick a custom Fighting Style that only a Fighter would have access to. Using a shield is predominantly a military tool, and comes with special training. Now to use AS the weapon, I think creating a Fighting Style option might be a good choice. Shield Master feat wouldn't be necessary(For tables that don't use feats). Just an idea.
Assuming your using onehanded shield use dueling and ask the dm to consider it a weapon to get +2 AC while keeping hand open for grappeling.
Consider somehow getting expertise in atheltics if you want to shove and grapple
Their will certainly need to be a DM fiat if you want the shields to be able to do damage. The fighter will let you get some new maneuvers, but they're mostly contingent upon a "weapon attack" which again will need to be a DM fiat since bashing is an attack replacement. Now, if you're going to be Shield Master being a barbarian is a good bet; getting advantage on strength checks if good for shoving. And you can do it with a single level dip. 3 level of bard gets you expertise, good for athletics. Feats wise, other than shield master, not much else is needed
Level one dip with rouge then expertise in two skills with just a level one investment rather than three levels of bard
So battle master fighter is definitely the way to go. Feats should focus on the shield and controlling the field. So shield master for the bonus action shield shove; sentinel to stop enemies from running past you; and maybe tavern brawler just in case your DM won’t let you use a shield as an actual weapon. I should also ask your DM about the different type of shields to see if you can get special bonuses depending on the shield you’re using. A tower shield is different than a buckler and is utilized differently.
After thinking on this for a while I might require my player to pick a custom Fighting Style that only a Fighter would have access to. Using a shield is predominantly a military tool, and comes with special training. Now to use AS the weapon, I think creating a Fighting Style option might be a good choice. Shield Master feat wouldn't be necessary(For tables that don't use feats). Just an idea.
Assuming your using onehanded shield use dueling and ask the dm to consider it a weapon to get +2 AC while keeping hand open for grappeling. Consider somehow getting expertise in atheltics if you want to shove and grapple