Sean Hollyman said:
I'd say Speech, Medicine and guns are the most important skills to level up.
With a high speech you can bypass most things easily, skip some bits, and get out of tight situations.
Medicine lets stimpaks and stuff do more, always handy.
And guns let you shoot stuff better.
First time I've ever been ninja'd by the OP, well played Hollyman, well played.
If I had to pick 3 apart from the ones you mentioned I would say
Unarmed - Ballistic Fist owns in New Vegas, plus you do not know how fun it is to choose bloody mess as a trait, name your character Kenshiro and only use the leather jacket as armour in Fallout 2. That shit is cash
Lockpick - Because, hey Im a kleptomaniac, sue me
Science - Without a decent science skill, FISTO will never be activated and sent to work the corners of Freeside