You want to use a shield and parry enemies so that you can smack them for more damage.

Fully level up a copper shield and you can pretty much beat trolls to death with your fists so long as you are parrying the troll's attacks.

there is a weapon that works with unarmed skill, its deep within the mountains so it's pretty good

Ah, didn't think about that, yes. For that weapon it makes sense.

Unarmed uses very little stamina which makes it good in some situations. You can quite easily beat the first 3 biomes without weapons but a good unarmed skill. It will take longer than with weapons tho, so I don't recommend it.
If you want to level unarmed just kill the elder or bonemass with fists. Bonemass will die quickly with a high unarmed skill tho, fists do blunt damage.

I find that if one has just a shield selected and you use unarmed, that it causes more damage then with out shield. Once you have leveled unarmed up to around 80 and using a shield you can cause allot of damage to Moder when it try's to pin you down. By blocking with shield and waylaying on Moder, you will see the amount of damage you can do.

Basically like Captain America using the shield.

It is pretty viable against lesser foes later in the game. For example, skeletons receive decent damage.

Killing greylings, necks, boars and other weaker enemies are great to start out levelling. Just mix it up in your gameplay.

I wouldn't bother. Damage output is just too low, especially later in the game. Good for messing around with poor Greylings, Necks and Boars, but not much more.