Good advice Do'tirath :tops: .
I do tend to keep only a few weapons as well on most roles though1 rifle, 1 pistol, 1 big gun / sniper / back up.
Also tend to not use any stimpacks, and no healing in combat at all.

It's a good challenge at the start on HC, very hard but ultimately I found at about mid way it's pretty smooth sailing. I found myself constantly forcing these artificial limits such as not carrying much loot and only a hand full of meds/ammo.

If your running the vanilla game I'd recommend not using any toughness perks or any implants, choosing small frame and sticking to light armour. If your doing a survival build I'd recommend trying not using fire arms and trying for a sneak/melee/explosives based character with ordinary weapons, meaning not resorting to using easy kill weapons eg.combat knife over ballistic fist. and poisons, which make an ordinary weapon like your combat knife still effective for ridiculous enemies.

Ideally I'd get your hands on some mods that tailor the game to what your after. GECKS is pretty easy to use to really up the challenge how you want.