Personal opinion; Depends on what type of battle your in. Close range on Fallout New Vegas I use probably either Old Glory (Lonesome Road) or Oh, Baby! simply because it saves bullets, and both of those (mostly Oh, Baby!) are highly effective. At my level, about 36, I use the Oh Baby to take out lone Deathclaws.
As for long range, recomend either an Anti-Material Rifle, a Marksman Carbine, or A Sniper Rifle. Especially when your fighting something like a ghoul or a typical wild mammal that has to come at you in order to injure you. As for humans, unless you think you can smash their head inside out your that close, recomended a gun, simply because humans even petty Raiders and Fiends have guns that can and will fire if they squeeze the trigger.
If you are gonna go with a hammar thing like a lets say a super hammar thing type deal, if your gonna use it, keep it's condition high, so you get maximum DAM so you might actually kill a Deathclaw before it kills you.
As well as have a high sneak.
If you are, watch out for landmines, its a pain in the crack especially when your at lower levels (aka, you probably just started) they (Not sure) can practically kill you in one, and at higher levels, they take away a lot of HP from the player.
So, if you go with Melee, keep your condition high, and well, as well has teach yourself to have a good eye for mines.