The main thing about leveling melee weapon skills is that it decreases your attack delay.
A weapons minimum delay is its base delay/2, rounded down to end in a 0, or 70%, whichever is lower.
So base delay 100% = min delay 50%, base delay 130% = min delay 60%, and base delay 200% = min delay 70%.
Note that the percent signs are misleading; I don't think it actually has anything to do with percents.
Each level of weapon skill decreases your attack delay by 5% until you reach min delay. Leveling past this point doesn't have much effect.
Fangs and claws and other body parts sometimes give you auxiliary attacks when you attack something. They also may affect which items you are able to equip or use.
Melee is good, but even a melee based character will want to delve into magic eventually for escape options.
Some combos you might want to try are Merfolk Transmuter, Draconian Wizard, maybe a Minotaur Berserker if you want an easy start.