Aerial units like dragons can only be hit by range weapons such as bows and arrows, and guns. Apart from that, it's mostly just about hit power - axes tend to just hit harder than swords etc. so you just want to pick the weapon with the highest attack.
However, when you level up you can choose perks that affect a specific weapon type and increase their power. This gets particularly interesting if you get to the 7th and 8th level of each perk. The perk that increases your attack power using your fists only, so no weapon, gets reeeally fun at the top two levels, for example :))
So, have a look through the perks, read what each one does, especially the highest level ones, and choose the ones that most suit your style of fighting.
