Could I use 4 luck and take the extra point for 7 agility?
Or do I need 4 luck for a future perk?
His will be my first time with an unarmed or explosives character, so I could use some pointers.
Maybe a list of what skills I should focus on and maybe the first few perks I should take.
I don't see a problem with having a luck of 4 and an agility of 7, in fact that would probably be better for you in the long run. I can't think of any explosives or unarmed perk that has to do with luck, and while critical hits can be fairly important for an unarmed character they are pretty much worthless to an explosives character.
The skills you should focus on should be:
1.) Unarmed (try to get this to 75 as quickly as possible so you can use uppercuts and crosses)
1.) Explosives
2.) Melee Weapons
3.) Sneak (helpful for getting closer to enemies without being detected and thus closing to unarmed range without taking damage)
4.) Repair
5.) Medicine (explosive cause a lot of collateral damage and unarmed fights lead to your character taking a lot of damage)
6-13.) Lockpick, Science, Speech, Survival, Barter, or what ever else you want to do with your character.
Perks you should get:
First of all, make sure you learn all of the special unarmed moves (Ranger take down, Legion Assault, Scribe Counter, and Khan Trick)
Other perks for early on:
Level 2 - Heave Ho!
Level 4 - Educated, Travel Light, or Cannibal
Level 6 - Demolition Expert (get all three ranks as you keep leveling up)
Level 8 - Stonewall
and Super Slam (make sure to get both as you continue to level up)
Level 10 - Nothing great here for your build, so go back and take another rank of demo expert or Stonewall/Super Slam
That should get you started with perks, after that just pick anything that benefits explosives and unarmed. Also make sure you get implant GRX, any perks that increase you DT, and I would also recommend Jury Rigging.
For companions I would recommend Boone and ED-E, although Rex would be fine as well. If you want to go the Legion route and you don't want Boone, then take Veronica early on and Raul later (give him a rifle)