Throw Anything with a Tower Shield
At a guess, if you’re going with Throw Anything applied to a Tower Shield, you’re looking at probably 1d12 or 2d6, i.e. one of the larger, heavier weapons. The weight isn’t even close, but I don’t know that a Huge greataxe (3d6) or whatever is really a good match even though the weight is closest.
For Captain America, though, you really want to be able to use shield bashes. You’re much better off using a Heavy Shield (after all, his shield doesn’t look like a Tower Shield or impose the kind of difficulties that Tower Shields do). Heavy Shields can be used as a weapon with shield bash, and can be enhanced with magic as a weapon separate from their magic shield enhancements.
It can also benefit from shield spikes, which are definitely a good idea. Captain America’s shield doesn’t have spikes; I’d ask my DM to allow a “studded” or “reinforced” shield that deals the same damage but as Bludgeoning damage. If you cannot get that, the difference between 1d6 and 1d4 is only 1 damage on average, so that’s not too bad, but the difference gets quite a bit larger as you increase in size (and you want to do that, it’s one of the best ways to improve shield bash damage).
+1 Ranged Shield
But I wouldn’t use Throw Anything; a +1 ranged shield would deal 1d8+Str points of bludgeoning damage when thrown, and return to your hand by your next turn. This doesn’t require a feat at all, which is very good, and it’s a shield enhancement (i.e. cheaper than a weapon enhancement), which is better. However, it cannot be applied to a tower shield. A +1 ranged heavy steel shield costs 4,170 gp.
The problem with ranged is that the 1d8+Str damage is fixed, and it’s very difficult to improve it. Things like shield spikes, weapon enhancements, or becoming Large or larger don’t work. It does count as a ranged weapon, so you can get some bonuses to it, but most shield-specific feats aren’t going to work.
+1 Throwing Returning Shield
At a +3 equivalent, a +1 throwing returning heavy spiked shield deals 1d6+Str+1 damage by default (equivalent, on average, to the +1 ranged shield), but you can add a lot more bonuses to this because size and weapon enhancements matter. The +1 throwing returning heavy spiked shield costs 18,330 gp though: that’s way too much for what you’re getting. It is a lot better than the ranged shield, but you don’t need to spend all that gold on it.
Instead, there are the Gloves of Taarnahm the Vigilant from Player’s Guide to Faerûn, which add throwing and returning to any weapon you have. They’re 10,000 gp, but the shield could be a +1 heavy spiked shield (2,330 gp), so your total (12,330 gp) is still massively less than the +1 throwing returning heavy spiked shield. The savings only improve from there if you add more weapon properties, which you should since if you have none the ranged shield is probably better.
A completely different alternative (but a popular one for Captain America, and a good choice in any event) is the Bloodstorm Blade from Tome of Battle. Among other things, it lets you apply throwing and returning to any weapon you like, without having to pay for it. It also has an ability to treat ranged attacks as melee attacks, which can mean very good things for the bonuses that you get to apply to them. Plus, it’s a Tome of Battle class, which means you have martial maneuvers. That makes you more versatile, skilled, and flexible than other martial classes (which are generally underpowered), which is generally a good thing.