Okay Stellarcell this is what I have in mind -- your character will be using the Fighter Class with the Battle Master Archetype but we are going to apply the Martial Artist alterations to it as follows:
Proficiency
... Armor : None
... Weapons : Simple Weapons, Martial Weapons
... Saves : Strength, Dexterity
... Skills : Choose 2 from Acrobatics, Animal Handling, Athletics, History, Insight, Intimidation, Perception, Stealth
Starting Equipment
... Longbow and 20 Arrows or Light Crossbow and 20 Bolts
... Two Martial Weapons
... One Simple Weapon
... Dungeoneer's Pack or Explorer's Pack
1st-Level -- Fighting Style is replaced with Martial Arts
Marital Arts
The character has gained mastery in combat styles that use unarmed strikes as well as weapons. The character gains the following benefits when not wearing armor nor using a shield.
• Their AC equals 10 + Dexterity Modifier + Proficiency Bonus
• All weapons the character uses have the Finesse attribute added to them.
• Unarmed Strikes do a d4 that improves to d6 at 5th, d8 at 11th, and d10 at 17th
• When using the Attack Action with an Unarmed Strike or a Weapon, the character can make an additional Unarmed Strike as a Bonus Action. Provided the character has not already taken a Bonus Action during that Turn.
Addition to Battle Master Maneuvers
Deflect Missiles
When another creature damages the character with a missile attack, the character can use their Reaction and expend one Superiority Die to reduce the damage taken by the number rolled on the Superiority Die + Dexterity Modifier. If the damage is reduced to 0, the character has the option to catch the missile provided they could catch such a missile and have the necessary hand(s) free to do so.
Note : You do not have to take Deflect Missiles I am just adding it in as an option in case you did want to take it.