I've also got to say that unlike the original, Melee and Unarmed are actually pretty fun in this game. The Super-Sledge sending people flying across the map, the Power Fist caving in skulls, the fact that additional levels in unarmed unlock "special moves", they can be quite entertaining.
There's a number more party members too, and you'll want to bring them along since they really make the game. Charisma determines party size, so a high charisma means you don't really need much in the way of combat skills depending on which allies you choose, even if you go guns blazing. (They can also accommodate for most of the other skills you lack, I believe, so that may be neither here nor there) And you really don't need to go guns blazing - I've beaten the game without ever launching an attack (though its not easy!). High Speech+High Science have some of the best and most fun bits, truth be told, but there really is fun for every build here, especially with some of the advanced Perks.
Oh, and Barter is worthless, don't tag that!
I think a very high agility+luck (crits!), decent charisma, decent strength character with melee (knives, yay!), speech, and stealth is a pretty fun build.
Outdoorsman is a fun skill, and super useful online, but not so much in the single player version. Lockpick and steal are good, but don't really need to be tagged except for a few special cases. First Aid and Doctor are useful, but aside from some special story bits stimpacks are moreso. Traps I rarely use, most of the combat skills are roughly equivalent, Gambling is broken to hell and back but infinite money isn't actually worth all that much...