The two major considerations a fighter must always contend with are armor and weapons. He has no spell list to consider in the morning, and once he has his feats he’s stuck with them.
Regardless of stylistic concerns, and within the boundaries of what is available to your fighter, damage output is always going to be important. Very little can be said about this that isn’t blatantly obvious.
For ranged purposes, nothing beats an old-fashioned bow for rate of fire. A fighter should use a Composite bow if available (as they have an increased range) and a strength bow if he would gain any advantage from it. The only consideration between a shortbow and a longbow should be whether you’re spending a lot of time on a mount. Mounted longbow archers just don’t cut it.
A dagger in the boot in case of emergencies is always to be recommended, but I’d hardly consider it to be a serious primary ranged weapon.
For melee, there are a few more factors to take into account. Taking the fighter’s intended feat path into account, make one of three choices: two weapons, one weapon and a shield, or two-handed.
The advantages of each are obvious. Two weapons yields an additional attack per round, two additional attacks per round at higher levels. Weapon & shield allows significant increases to armor class, making a fighter quite the tank. Two-handed weapons preclude the use of shields, but simply do the best damage available.
When dealing with two weapons, don’t bother pairing non-light weapons (two longswords, two battleaxes, etc) unless you’re dealing with poorly armored foes. The penalty to attack just doesn’t add up in an armored world. When frequently dealing with the heavily armored, don’t take any unneeded attack penalties.
With a light/medium weapon combo, use a Battleaxe and a Shortsword. The Battleaxe is mathematically substituted by the Longsword or Warhammer. The Shortsword is analagous to the handaxe. Any combo will do, so make the decision stylisticly.
The disadvantage of the two-weapon path is the number of feats required just to make it efficient. To get a -2 to all your attacks, you need to have a medium and light weapon, ambidexterity, and two-weapon fighting. To get a second attack with the off-hand weapon, you need improved two-weapon fighting. This takes a lot out of an otherwise quick feat progression.
Weapon & Shield
For the low-dexterity fighter who doesn’t want to get hit too often, this is probably the way to go. Get yourself a warhammer, longsword, or battleaxe, a set of full plate, and a large shield, and you’ve got excellent protection and mediocre damage at your fingertips. Very little is more frustrating to folks that have a +10 attack bonus like running into an opponent with over a 26 AC. After chopping through chumps with greatswords and banded mail like butter, being reduced to a 25% chance of landing a blow can be quite demoralizing.
The only disadvantage to this option is the lack of the other two options’ damage-dealing potential.
For a strong fighter hell-bent on dealing out damage in big regular doses, the Greatsword is hard to pass up. 2d6 damage with a 2x threaten on 19 or 20. Add in 1.5x the strength bonus to damage and you’re looking at serious average output per attack.
The route doesn’t quite have the damage potential of the two-weapon fighting, but you can jump straight into it without any prerequisite feats or attack penalties. A straight-math breakdown on Longsword/Shortsword combo vs. Greatsword is in progress at the moment.
It appears from some preliminary number-crunching that the two-weapon style only outmatches the two-handed weapon or the weapon & shield combo only when all multiweapon feats are involved, and even then only with exotic weapons such as the Orcish Double-Axe (which do longsword or battleaxe-style damage with each attack but are considered a medium/light combo for attack bonus purposes)