Nuclear Physicist, Nerd Rage, and Heavy Gunner are the best perks for a Brotherhood of Steel Build because they help increase damage and reduce damage taken. Nuclear Physicist makes staying in Power Armor much easier. Nerd Rage gives you a “oh crap” moment when taking a big chunk of damage and slows time down. Heavy Gunner is your weapon damage perk for using heavy Miniguns or Gatling Lasers.
Here is the list of the best and recommended Perks for the Brotherhood of Steel Build in Fallout 4:
Nuclear Physicist – best perk when using Power Armor consistently.
Nerd Rage – the best damage reduction perk outside of Lone Wanderer (no companion).
Science – a needed crafting perk to make the most advanced Power Armor mods.
Heavy Gunner – increases heavy weapon damage, though you can use Rifleman or Commando if you prefer.
Demolition Expert – makes explosives do more damage, including your weapons and stacks with other perks.