Overall there are not many enchantments you can use that would be considered the best for shields in Minecraft. However, there is two that would be the best to put on, and the first is mending, second is unbreaking.
Mending is a useful enchantment that will take experience orbs you gain from doing various activities and use them to repair your enchanted object when placed on an item.
For that reason, we would recommend using it on the shield as you are bound to be fighting monsters, so the XP orbs could go to keeping you protected with your shield longer in fights.
Related: Best Minecraft Shovel Enchantments
You can also, in turn, combine this with unbreaking if keeping your shield usable is your goal in the game.
The reason why is that unbreaking will increase the durability of whatever item it's on, so if you place it on your shield, it will last longer. Then when combined with mending, it will take less to repair your shield via XP orbs.
Overall, it's not very practical to enchant shield, as if you have decently enchanted armor, that would be fine enough. However, if you want to enchant your shield, your best bet would be going with these two enchantments.
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