Claws would be a good power to buy. Lethal Weapon is okay, but Claws outclasses it. Armed Arts might be able to compete with Claws, but I'd rather have the power.
The Martial Artist stunt is pretty much mandatory.
You have a tough choice about defence here. Fists or Athletics? Whether or not you want Speed will make a big difference to this choice.
If you pick Fists, Footwork is probably a good idea.
Beyond that...make your own stunts. Sticking to canon stunts is crazy. Your Story explicitly tells you not to do it.
If you need inspiration, here's the Fists section of the revised homebrew stunt list:
Fists:
Patterns: Martial arts are actually a lot like dancing. You may use Fists instead of Performance to demonstrate martial arts moves.
Competition Fighting: You are a martial artist, not a fighter. Add one to your Fists skill as long as you aren't in a real fight.
Board Breaking: You break stuff with your hands. You may use your Fists skill for the Breaking Things trapping of the Might skill.
Street Fighter: You don't fight by the rules. If there's a piece of lead pipe lying around, you'll use it. You may use your Fists skill to wield improvised weapons.
No Holds Barred Beatdown: What’s the opposite of mercy? Whatever it is, you show plenty of it in your fights. All of your attacks with Fists inflict X additional stress, where X is the level of the worst consequence that you have inflicted on the target this scene. (A similar stunt could exist in Guns or in Weapons.)
Use Their Strength Against Them: Excessive strength can be a disadvantage if your opponent knows how to exploit it. Add one to your Fists skill when using it to attack, defend against, or block the actions of a character whose Might skill is greater than your Fists skill. (A similar stunt could exist in Weapons.)
Nasty Infighter: You practice judo or another grappling-based martial art. You may use your Fists skill for the Wrestling trapping of the Might skill.
Throws And Holds: (Requires Nasty Infighter) If you aren’t careful when attacking a wrestler, you’ll end up on the ground. On a successful close-combat defence with Fists, you may sacrifice your next action and invoke one of the attacker's aspects in order to turn that defence into an immediate grapple against the attacker with a strength equal to your defence roll. This grapple does not need to be renewed until you act again.
Guard Breaker: You have a talent for getting around certain types of defence. Pick a skill. Add one to your Fists skill when attacking someone who is using that skill to defend. (A similar stunt could exist in Guns or in Weapons.)
Potent Poison: The poison produced by your body is exceptionally powerful. Add one to your Fists skill for any use of the Venomous trapping of the Claws power.*
Destroyer Of Abominations: You hit harder when your enemy is something blasphemous. All attacks that you make with the Fists skill inflict two additional stress to creatures that are in some way unusually offensive to your faith. (A similar stunt could exist in Guns or in Weapons.)
Kick The Bruise: It really hurts to take two hits to the same place. Whenever you tag or invoke a consequence to benefit a Fists attack, that attack inflicts two extra stress. (A similar stunt could exist in Guns or in Weapons.)
Storm Of Punches: A great warrior fights as well against a thousand enemies as he does against one. You may make spray attacks with your Fists skill.
Demesne-Assisted Combat Focus: It's easy to win a fight when you control the world around you. Add one to your Fists skill when using to attack as long as you are in your Demesne. (A similar stunt could exist in Guns or in Weapons.)*
Demesne-Assisted Combat Specialization: It's easy to win a fight when you control the world around you. As long as you are in your Demesne, your Fists attacks inflict two additional stress. (A similar stunt could exist in Guns or in Weapons.)*
Bull Charge: You know how to use your momentum in a fight. If you move at least one zone as a supplemental action before making an attack with Fists, that attack inflicts two additional stress. (A similar stunt could exist in Guns or in Weapons.)
Talking With Your Fists: A guy with the ability to hurt you is always scary, even if he's got no charisma at all. You may use your Fists skill instead of your Intimidation skill when threatening someone with violence. (A similar stunt could exist in Guns or in Weapons.)
Unorthodox Fighting: People with formal training are less able to defend against your tomfoolery in combat. Add one to your Fists skill when making attacks against opponents who adhere strictly to a formal style of combat. (A similar stunt could exist in Guns or in Weapons.)
Give As Good As I Get: Sometimes, you have to do something crazy in order to win a fight. Once per scene, when you are attacked, you may spend a Fate Point. If you do so, you defend against the attack with an effective skill of Mediocre and may not use a Block to replace your defense roll. This might sound pretty grim, but take heart; if you attack your attacker with your Fists skill during your next action, you may add three to your attack roll and increase the weapon rating of your attack by three. (A similar stunt could exist in Weapons or in Guns.)