Go melee, it made the game insanely fun. Focus on getting high endurance so you can get all the implants, and then just run straight to New Vegas going north (Like the prior games, the enemies can not scale anything that requires a little jump, so if you stick to the jagged rocks, all Deathclaws and other nasties will just suddenly run off because their AI doesn't know how to reach you.)
Get a high luck (7+, if not 9), as Luck increases all your skills. Make sure you don't get XP until you have the intelligence implant, as you will get the most skillpoints then. Start playing in the deadbeat casino in the Atomic wrangler, break the bank, then you'll have enough money to go to Vegas and become filthy rich within seconds.
If you want to, you can build an unbeatable killing machine with the right melee perks. Getting the one that allows every melee and unarmed attack to ignore damage threshold (-15 to be exact), makes every normally "hard" foe a joke. (mowing packs of Deathclaws down like they were brahmin)
Play on the hardest difficulty, as it is so much more satisfying going through every enemy like butter when you know it can't get harder than this with your special fire-axe (Knock Knock!).
EDIT:
For added fun, get the spiked knuckles and pretend you're playing DOOM II after picking up the Berserk powerup. Just like in Doom, everything you touch turns to giblets.
Also, if you want your character to be a beast in both unarmed and melee, you will have to sacrifice some perks that make you harder to kill in favor of damage perks. That's no problem though, just get a companion to tank for you, then load up some psycho and slasher and go to town with whatever melee weapon you have and everything in the game will die.