I'll also tag on to Panando's TLDR and say if you had to choose only one, picks would be fine, though shortswords are my first generalist choice.
I had good reason to recommend Picks, based on some tests. And I just did another more rigorous test with weak Novice combat skill dwarves, and picks had a very clear advantage.
This test involved a Dwarf with stats only 70% as high as a normal dwarf, resulting in a description like:
Their mental stats were also only 70% as good as a normal dwarf.
The target dummy was a Goblin with normal stats, standardized at 100% size, and fully clad in iron armor. I used a target dummy because otherwise some weapons are going to have good consistency in winning and others will just get destroyed nearly every time, failing to capture just how large the performance difference is between weapons.
Number of combat actions required for the weak, low skilled Dwarf to destroy the Ironclad Goblin:
| weapon | mean | stdev | confidence_level | margin_of_error | lower_bound | upper_bound |
|---------------------|--------|--------|------------------|-----------------|-------------|-------------|
| ☼steel pick☼ | 13.73 | 7.02 | 0.95 | 1.38 | 12.35 | 15.11 |
| ☼steel short sword☼ | 17.54 | 10.62 | 0.95 | 2.08 | 15.46 | 19.62 |
| ☼steel spear☼ | 20.91 | 11.45 | 0.95 | 2.24 | 18.67 | 23.15 |
| ☼steel battle axe☼ | 31.82 | 17.15 | 0.95 | 3.36 | 28.46 | 35.18 |
| iron whip | 46.28 | 31.96 | 0.95 | 6.26 | 40.02 | 52.54 |
| iron morningstar | 129.98 | 85.24 | 0.95 | 16.71 | 113.27 | 146.69 |
| ☼steel war hammer☼ | 140.11 | 56.56 | 0.95 | 11.09 | 129.02 | 151.20 |
| iron scourge | 166.42 | 81.21 | 0.95 | 15.92 | 150.50 | 182.34 |
| ☼steel mace☼ | 245.50 | 128.93 | 0.95 | 25.27 | 220.23 | 270.77 |
(As a note, the Whip actually takes about 15% longer than the "action count" because of its slower speed, so its actual mean is more like 54)
The Steel Short Sword is second best, but the Pick is still best and by a fair margin!
But also check out just how much more bad the Steel Mace is! It took fully 18x longer for the Mace Dwarf to destroy the Goblin than the Steel Pick Dwarf, in fact the Macedwarves would often pass out from exhaustion before killing the Goblin!
This kind of 1v1 performance difference can be square-rooted to get a very approximate comparison, e.g. sqrt(18) = 4.2, meaning that 1 Pickdwarf is worth 4.2 Macedwarves or a Pick is 4.2x better than a Mace in the hands of an unskilled weak dwarf. This is simplified of course, because a mace blow might be able to cripple an enemy, and then a dwarf with a more effective weapon might join the fight and deal the finishing blow, but there's little evidence that Maces are better at crippling than de-limbing weapons are.
It's insane how much better the edged weapons do against these heavily armored Goblins, the conventional wisdom is that blunt weapons should do better. Conventional wisdom is the Battle Axe should do poorly, and indeed it did do poorly relative to the "impaling" weapons but it still did better than any bludgeoning weapon by a large margin. This edged advantage is mostly due to the extreme awesomeness of Steel relative to Iron.
Now why did the Pick do best?
It's because of the velocity multiplier! A Pick has a Velocity Multiplier of 2x, compared with 1.25x for Sword and Axe, and 1x for Spear. The velocity multiplier directly increases momentum. Picks, Axes and Swords all have different contact areas, but when hitting small things like Goblin limbs the contact area is generally "min'd" with the limb diameter (perhaps applying some basic trig to account for strikes at a bad angle), so effectively all three weapons end up with the same contact area for a good hit on a limb, but the Pick is hitting considerably harder, cutting through the armor and limb more easily. The Spear and Short Sword are probably out-performing the Axe for a different reason: their stab contact area is small and easily goes through the armor when hitting larger parts like the body.
Check out the deflections statistics:
| Weapon | action | deflect | total | ratio |
|---------------------|---------|---------|-------|-------|
| ☼steel pick☼ | strikes | 0 | 807 | 0.0 |
| ☼steel short sword☼ | stabs | 0 | 494 | 0.0 |
| ☼steel spear☼ | stabs | 0 | 1312 | 0.0 |
| iron whip | lashes | 0 | 2768 | 0.0 |
| ☼steel battle axe☼ | hacks | 304 | 1811 | 16.8 |
| ☼steel short sword☼ | slashes | 109 | 537 | 20.3 |
| ☼steel mace☼ | bashes | 5857 | 16418 | 35.7 |
| ☼steel short sword☼ | slaps | 10 | 27 | 37.0 |
| iron morningstar | bashes | 3081 | 7586 | 40.6 |
| ☼steel war hammer☼ | bashes | 3505 | 8608 | 40.7 |
| ☼steel spear☼ | bashes | 21 | 50 | 42.0 |
| iron scourge | lashes | 4349 | 9668 | 45.0 |
| iron morningstar | strikes | 262 | 482 | 54.4 |
| ☼steel battle axe☼ | slaps | 47 | 86 | 54.7 |
| ☼steel short sword☼ | strikes | 22 | 38 | 57.9 |
| ☼steel battle axe☼ | strikes | 47 | 78 | 60.3 |
Now, the Sword, Battle Axe and Spear all get lots of deflections for their "joke" attacks like slapping, but Dwarves don't perform this action very often at all.
When we look at the real attacks, that are chosen ~95% of the time, we see a substantial disparity. The Pick and Spear
never deflect, they slice through that puny iron armor every single time even in the hands of an unskilled weakling, that doesn't mean the armor does nothing, it still reduces the momentum getting through to the flesh, but it sure can't stop these weapons. The Short Sword Stab also never gets deflected, but it's slash does get deflected 20% of the time. The Battle Axe's hack gets deflected less often than the Short Sword slash, this could be because it's a heavier weapon, or it might just be statistical noise, but in any case, half of the Short Sword attacks are just not getting deflected at all which puts it ahead, and all of the Battle Axe's attacks are getting somewhat dampened by the armor - in fact considering the overall performance weakness of the Axe, they're probably being greatly dampened even if it does get through to the flesh. Also more than half of the axe deflections are to the body, where there's a much larger possible contact area and 100% of hacks to the body were deflected, this is precluding injuries to the heart or lungs. Also 50% of hacks to the head were deflected greatly reducing brain injuries. In contrast, only about 10% of hits to the limbs were deflected. The axe basically has to kill by decapitation or blood loss due to limb removal, whereas the stabbing weapons have more possibilities especially heart and brain injury.
The Mace and Hammer also get deflected quite a bit, but that's not really why they are bad, in fact weapons can still do joint/neck damage on deflections when hitting small things like heads and hands. They're clearly bad because they have trouble doing catastrophic damage, they have trouble rendering the goblin unconsciousness, and have trouble breaking through the helm.
Anyway, TL;DR, back to the Pick.
In no high quality test have I ever seen the Pick got surpassed by another weapon except perhaps the Spear against extremely large tough opponents but in that case it tends to vastly out-perform the axe or sword. It'll often be tied in first place with the spear, or the axe and sword, depending on enemy type. But it's 2x velocity multiplier just makes it the best edged weapon, hitting as hard as a blunt weapon but causing deep stabbing wounds. This effect is going to be most obvious when the dwarves are weak relative to the toughness of the thing they are hitting meaning overkill isn't a factor. Since overkill does become a large factor with fully trained military dwarves, it basically means Pick is the best weapon for recruits press-ganged into a fight, but there's not a major disadvantage to using axes or swords for your career military since they'll be hitting so hard that any slicing weapon will do devastating damage on every hit.
Also if you let dwarves be Macedwarves, AT LEAST issue them morningstars at first opportunity. I've pretty much never seen the mace outperform the morningstar, but in a number of tests the morningstar has significantly out-performed the mace. Not enough to make it actually good, but still better than the mace. The morningstar penetration stat is very small, meaning that it doesn't do much bleeding injury before the momentum is converted into bludgeoning exactly like a mace, it really behaves exactly like a mace or hammer against unarmored opponents, but against armored opponents it can "2x" the mace, I suspect some quirk of penetration mechanics is at work: what I think happens is that the tiny spike on the morningstar penetrates the armor, then the penetration depth runs out, but now it's through the armor, and all the blunt force trauma is delivered to the flesh instead of having to transmit through the armor, this doesn't exactly make sense in terms of real life physics but I'm pretty sure it's what is happening. (incidentally, I also tested a steel masterwork morningstar, and it did better than the axe! This indicates that with the extra penetration ability of steel its momentum was pretty much completely bypassing the armor, also reflected in deflections being completely eliminated. Pity you can't make them in fortress mode.)