So using your fists as your munk weapon and take 3 levels into fighter and take the champion subclass for fighter. You crit with your weapon on a 19 or 20. Can you still crit wit a 19 on an unarmed attack? Because you technically aren't using a weapon. 

Since it specifies weapon attack then I would say no, it doesn’t count on unarmed strikes, but would work with any Monk weapon you might be using. 

According to the sage advice compendium unarmed strikes count as melee weapon attacks despite not being weapons. It’s under the monk section talking about stunning strikes. 

With that being the case I would say that they do count for the champion abilities and even smites. 

I did not realize this. Thanks for that. 

it got me excited thinking you might be able to use it with green flame blade or booming blade but the cantrips specifically say with a weapon, and the Sage Advice say it is a special type of melee weapon attack even though it is not a weapon. Hopes dashed.