Did you know about that special rule?
You get double damage with melee while in VATS. That helps a lot while on Very Hard.
As for OP:
If you are new to the game this is the recommended order for weapons and weapon skills -
1. Guns
2. Energy
3. Explosives
4. Melee
5. Unarmed
For a first timer, I recommend selling energy weapons and ammo, and all explosives except hand grenades. You will need the money for a set of Combat Armor Mark II and repairs.
All skills work much better with Stealth. But its especially good with explosives if you wanna setup mines and remote C4. Make some traps, kill a bunch of enemies with the initial explosion, pick off the leftovers with a grenade or grenade launcher while sneaking.
Be careful of giving your companions explosives, they tend to go a little crazy and often hit you. And they also tend to spray ammo liberally so if you give them a weapon, consider something slow to fire and reload, like the sniper rifle, or even better the Gobi Campaign.
Lily has infinite ammo for her M-16 so just leave her alone.