Things to Think About

Build a character as if they were a normal person living in the world. Don't min-max; real people don't live that way. And keep in mind their daily lives that occurred before they were scooped up by Fate and turned into a Player Character...what skills did they have that allowed them to hold down their job? What did they learn growing up? They don't have to be experts at those things, but a handful of points put into "everyday skills" can go a long way to making a good character that could survive in the world.
The below list is a good thing to keep in mind...you don't need all of the skills, but having a few of them might prove useful.
(This list is from Kromm, aka Sean Punch)
Relying on defaults -- whatever the game system calls them -- is rarely fun. In GURPS, I hint that certain skills are necessary for adventurers, true action heroes or not, to keep the story flowing without annoying breaks caused by PCs being incompetent at tasks that adventure fiction commonly treats as "everyman" skills:

• Carousing, Diplomacy, Fast-Talk, or Interrogation -- Eventually, everybody wants to interrogate NPCs. I'm generous about what skills work, but some skill is required.

• Climbing, Hiking, and Stealth -- The party is only as good at these things as its worst party member, and nearly every party has to move around as a unit at some point.

• Driving or Riding -- Travel is vital to adventure, and while "every hero can drive/ride a horse" is often assumed, it isn't automatic in games that have skills for these things.

• First Aid -- Effective bandaging isn't an unskilled activity, AD&D notwithstanding. Non-action heroes often want to do this to "contribute" to party combat effectiveness, so they especially need this skill.

• Gesture -- Sooner or later, communication without making a sound will be vital to almost any party's survival.

• Observation, Scrounging, or Search -- Noticing interesting things takes training, and finding clues and useful items is so central to adventures that no PC should lack at least basic training here.

• Savoir-Faire or Streetwise -- Everybody came from somewhere. It's passing annoying when a player just assumes that her PC would "get on with folks in her element" without having any practical social skills to back up the assumption.

I further suggest -- strongly -- that action heroes have this list as well:

• Axe/Mace, Broadsword, Knife, Shortsword, or Staff -- Wielding a stick, knife, or heavy tool to any real effect requires practice. These common improvised weapons are not idiot-proof, trivial, or safe to use without training.

• Beam Weapons, Bow, Crossbow, or Guns -- However easy "point and shoot" looks, it's quite tough in reality. No credible action hero lacks competency at all ranged combat.

• Boxing, Brawling, or Karate -- Fisticuffs are the worst place to be untrained. Your fists are the only weapons you always have, so learn to use them.

• Forced Entry -- No, it isn't easy to kick in a door. Actually, unless you know how, you'll hurt yourself.

• Holdout -- "Concealable" equipment only works if you have skill at concealment, and frustratingly few players realize this.

• Judo, Sumo Wrestling, or Wrestling -- The number of people who think they should be able to grab others automatically is astounding. In fact, this is a difficult feat, trickier than hitting people, and absolutely requires training.

• Throwing -- Whether you're tossing spare magazines to friends or grenades at enemies, this is a trained skill, so it pays to know it.

I think that players would be far less unhappy about surprises if more GMs made lists like this and did everything possible to get players to take them seriously. A PC with Brawling, Fast-Talk, Forced Entry, Holdout, Knife, Scrounging, Stealth, and Wrestling should be able to make and conceal a shiv, overpower a guard, steal his clothes, sneak away from the scene, talk his way past the other guards, and leave through an inadequately bolted back door.