In general, a PC with higher Strength will do more damage with a given weapon. There seems to be one important exception to this: whips. As implemented in ADOM, the damage done with whips, especially dual-wielded whips, seems to be more dependent on Dexterity than Strength. The manual touches on this subject, stating that a PC must have high speed to use two whips effectively. Dexterity seems to be at least as important.
0.7.1 Jack of all trades or master of one?
This is a matter of personal preference and style. The advantage of becoming very proficient with one weapon becomes clear from reading the manual: bonuses to the to-hit and to-damage as well as reduced attack cost when using the weapon. There is also the possibility of achieving Grand Mastery, where the attack cost is reduced to the point where about 1 1/2 attacks per round is possible. The downside is also easy to imagine: without an artifact weapon in the specialized category, a PC can have the weapon destroyed and be without one. In practice this is not usually a problem since there are generally plenty of weapons to be found in the game. Also, a PC may run across a truly outstanding weapon at some point in the game, some of which are guaranteed, and have no skill with the weapon. Again, this is not usually a huge problem since mid- to high-level PC's will be able to train up their weapon skill in any given category relatively quickly.
Critical hits yield double skill marks. If the PC finds a weapon that delivers critical hits, it will train twice as fast.
0.7.2 Class considerations - what weapon to specialize in
Beastfighters - Beastfighters receive severe penalties for using melee weapons, and should avoid doing so for this reason. They develop a formidable unarmed attack as they advance in experience and Unarmed Combat skill. Note that the penalty does not apply to missile weapons; all beastfighters should practice with missile weapons in order to take advantage of -foo- slaying ammunition.
Mindcrafters - Willpower is critical for Mindcrafters. The Sword of Nonnak is a guaranteed artifact sword available to most PCs at experience level 15 or less. It grants +5 to Willpower. This makes Swords an attractive weapon class for Mindcrafters to specialize in, at least during the early game.
Monks - Monks also receive penalties for using weapons, albeit not as severe as Beastfighters, and so should specialize in Unarmed Combat. Monks also excel at kicking and receive a class power that enables them to deliver a circular kick.
0.7.3 Achieving Grand Mastery
Grand Mastery is difficult to achieve. It will not happen simply from using a single weapon type throughout a normal game. Becoming doomed in the wilderness for the frequent wilderness encounters is one way of generating an infinite number of enemies to be killed with no corruption. The Crown of Science (doubly useful because of its +9 bonus to Le) or a ring of doom can be used for this.
There is one class + starsign combination that can reasonably expect to achieve Grand Mastery during a normal game. Note the following two manual entries:
From the Weapon Skills section:
Farmers are so skilled in the use of polearms that they need 20% less marks to increase in their use.
From the Horoscope section:
Positive modifiers from Tactics settings are increased by 10%, costs to increase melee weapon skills are reduced by 20%, +1 to the initial Learning score.
This double 20% reduction in cost to increase weapon skills means that farmers born in the month of the Sword who use polearms exclusively, and do not hurry, can expect to achieve Grand Mastery with polearms. This will happen approximately by the time the PC reaches the Mana Temple, depending on the ending the PC is going for, etc.