In contrary to Froggy's comments, I have never once had any trouble what so ever with fast travel. Once a static enemy dies, they stay dead for the entire game. Unless you're playing a total pacifist, you won't have any trouble going back to areas that were previously explored. The exception to this is apparently Deathclaws, which repop every time I traveled to that area (Old Olney, I think).

Playing a close combat character is world's different than playing a run-and-gun character. In contrary, again, early levels are surprisingly easy for a CC. It's the later levels that will kick your butt, as everyone and their grandmother will have rifles and variations of combat or power armor. The worst are the missile launcher-equipped enemies or enemies with frag grenades. The choice of playing either Unarmed or Melee is up to the player, but it all boils down to how early you can get a Ripper/Super Sledge or a Deathclaw Gauntlet. Another choice is if you want to spend perks on Iron Fist increasing your Unarmed damage (by a HUGE amount), or go Melee and spend those perks elsewhere. Either build you choose, building up both skills for Ninja is a requirement. Paralyzing Palm may seem cool, but having to throw away your Unarmed weapon (Deathclaw Gauntlet, Power Fist, etc) just doesn't make it all that worthwhile.
Another thing to note about close combat characters is that followers = life. They kill things often more quickly than a ranged character, and have a ton of hit points. Keep them alive, and they will keep you alive. If you have good karma, picking up Fawkes at the end game is a VERY good idea. He can mow down anything in his path. Both ends of the karma spectrum can pick up the ghoul follower in the Underworld.

And I've never once bothered with Luck, except for purposes of getting the 6 Luck requirement needed for a few perks. An extra 1% critical chance is not worth sacrificing an additional 10 to your carry limit. Besides, with a good sneak, you will get an automatic critical with bonus damage if you land a sneak attack, often enough to kill the enemy outright. I usually start with 4 Luck, spend a perk to increase it once, and find a bobblehead.