Attack roll for unarmed strikes = d20 + proficiency bonus + Strength modifier.

Unarmed strikes are, in fact, melee weapon attacks - even though they're not made with a weapon. This is clarified in the Sage Advice Compendium:

What does “melee weapon attack” mean: a melee attack with a weapon or an attack with a melee weapon?

It means a melee attack with a weapon. Similarly, “ranged weapon attack” means a ranged attack with a weapon. Some attacks count as a melee or ranged weapon attack even if a weapon isn’t involved, as specified in the text of those attacks. For example, an unarmed strike counts as a melee weapon attack, even though the attacker’s body isn’t considered a weapon.

Here’s a bit of wording minutia: we would write “melee-weapon attack” (with a hyphen) if we meant an attack with a melee weapon.

This is also supported by the fact that the rules on unarmed strikes are stated in the the "Melee Attacks" section of the rules; the wording is simply clarifying that if you want to make a melee weapon attack without a weapon, you can use an unarmed strike to do so.

As such, the attack roll is calculated as follows:

• d20 + proficiency bonus + Strength modifier

Try creating it off of a weapon template such as a javelin

I don't think you will be able to create what you want with a shield. However if you made it a weapon template, then added an AC bonus modifier when equipped, it would essentially function as the weaponized shield that you want.

Rename the text of the javelin to be your shield so it shows up how you want it on your character sheet!

I just ran through it real quick on my phone: When using the javelin template, add Modifier Type: Bonus and Modifier Subtype: Armor Class and you can give it the Fixed Value of 2

To add even further to it: In order to make this truly Captain America's shield, you could create a Weapon Bond like the Eldritch Knight gains access to at the 3rd level

Once you have bonded a weapon to yourself, you can't be disarmed of that weapon unless you are incapacitated. If it is on the same plane of existence, you can summon that weapon as a bonus action on your turn, causing it to teleport instantly to your hand.

So you could essentially throw it as a ranged weapon, have it teleport back into your hand, and still give you the +2 AC for having a shield. It should however be noted that your AC would be -2 once you throw it until it is back into your hand.