Some maneuvers state

1)  Requires a weapon attack.

2) Requires a Melee weapon attack.

Using Unarmed Fighting Style or a Monk's Martial Arts.  Can I use option 1 and 2 or Just Option 1

Are unnamed attacks considered weapon attacks or melee weapon attacks?

Unarmed strikes are special types of melee weapon attacks, so they would qualify for both 1 and 2.

As already stated, an unarmed strike qualifies as a melee weapon attack.  However, if there is something that specifically requires the use of a weapon then an unarmed strike would not qualify.  Here is the rule:

Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons).

Thank you.

Basically the "weapon" in "weapon attack" exists to distinguish if from a "magic attack". Any attack roll is either a weapon attack or a magic attack.

Most Battle Master maneuvers should work with unarmed strikes except for ones like Brace which requires you are wielding a melee weapon (though would work with a monk weapon). If it says when you make a weapon attack or melee weapon attack it works. 

Quote from ThriKreenWarrior >>

Most Battle Master maneuvers should work with unarmed strikes except for ones like Brace which requires you are wielding a melee weapon (though would work with a monk weapon). If it says when you make a weapon attack or melee weapon attack it works. 

Well no, the rules are bit more stupid than that unfortunately.
An unarmed strike is not a weapon. So for anything that says "weapon attack" or "attack with a weapon" then an unarmed strike will not qualify.
However unarmed strikes are specifically called out to qualify as a "melee weapon attack".

However for most things that is a flavour/lore choice from the designers and not a balance issue so if a DM want to houserule it differently then go right ahead.

Quote from Thezzaruz >>

Quote from ThriKreenWarrior >>

Most Battle Master maneuvers should work with unarmed strikes except for ones like Brace which requires you are wielding a melee weapon (though would work with a monk weapon). If it says when you make a weapon attack or melee weapon attack it works. 

Well no, the rules are bit more stupid than that unfortunately.
An unarmed strike is not a weapon. So for anything that says "weapon attack" or "attack with a weapon" then an unarmed strike will not qualify.
However unarmed strikes are specifically called out to qualify as a "melee weapon attack".

However for most things that is a flavour/lore choice from the designers and not a balance issue so if a DM want to houserule it differently then go right ahead.

Since unarmed strikes are melee weapon attacks, and melee weapon attack is a subcategory of weapon attack, they actually do qualify for things that say "weapon attack". As you said, though, they don't qualify for something that says "attack with a weapon". Thri-Kreen was right.

It says weapon attack because they apply to both melee and ranged weapon attacks.

The “attack with a melee weapon” phrase would not qualify and I don’t recall if there are any maneuvers that have that wording.