Originally my approach was purely ranged based, carried over from Fallout 3. I divided enemies and weapons into 3 categories; long, medium, close. For long range, I used Ol' Painless - in NV finding the Sniper Rifle to be the best choice. For medium encounters, I used the unique Chinese Assault Rifle - it doesn't have a direct anologue in NV, so the Cowboy Repeater I found was best. Up close I used either Blackhawk or The Terrible Shotgun, replacing them in NV with the Riot Shotgun.
However, the increased levels and perks mean that The Courier can be a lot more nuanced than The Lone Wanderer - there are more approaches. With hardcoe mode weight becomes a big issue; Unarmed and Melee far more valuable. Following the release of Honest Hearts, I ditched all my gear and rethought my entire combat approach, so that The Courier can equip any weapon in any situation taking minimum damage.
It boils down to four interconnected states. Detected or undetected, at range or up close - based on a new-found appreciation of Sneak that Zion impressed upon me.
Undetected at range, I use a silenced Colt .45 pistol - quick, fairly accurate and with the Grunt perk and Better Criticals absolutely lethal attacking from stealth. The one shot, one kill technique means I don't carry that much ammunition - this isn't a weapon for protracted firefights.
Undetected up close, Chance's Knife. With Cowboy and Grunt perks its base damage gets a hefty boost. Silent and deadly, it allows The Courier with Silent Running to brutally dispatch a building full of enemies before the first man arrives in Hell.
Detected at range, I equip the All-American for two reasons - accuracy and ammunition availability. A few well placed shots to the temple usually fells any enemy before they can close, although priority is given to enemies which can attack from range. A gunman should always eliminate the greatest threat first. If any make it to me alive, there's...
Detected up close, it's Ballistic Fist time. It is right to learn, even from the enemy - Caesar's Praetorians taught me a fearful lesson in slaughter the first time I stormed his tent. The power of the Ballistic Fist combined with the deadly rush of the Legion Assault means enemies that close within your circle will be dead within seconds. Piercing Strike puts even Deathclaws to shame.
With this setup, I have only two weapons requiring ammunition and no need of any heavy armour, leaving plenty of space for juicy DLC loot. Pretty much any situation can be met instantly with deadly force based on the above formula. The only real threats are explosive wielding enemies - Powder Gangers, for example, can sometimes get off a stick of dynamite before they can be dispatched. Lighter armour means The Courier with this may take more damage that those with other philosophies. Large crowds including those wielding Grenade Launchers are also a problem - the philosophy is based on deadly accuracy, initially attacking from the shadows to pick off enemies one by one. Overwhelming displays of force and crowd suppression tactics are not my forté with this build - I carry no explosives, for instance. However, I compensate via hotkeyed StimPaks and 100 Medicine, as well as the 2 ranks of Toughness.
So, you're heading to an area where you expect a fight. How do you approach it?