I mean you are out of mana, running around doing nothing feels a bit stupid when you can equip a weapon and do some damage. What weapon feels right to use as a mage ?

There are staves, but they don't act as weapons at all, more like wands. NPC mages use daggers, that's one option, but using the dagger for both attacking and defending ... you can't bind that to hotkeys and the range I assume is a bit too "in your face" dangerous. Then there are 2h weapons Sword is the fastest, that's probably the best option in that regard.

So what about it ? Should pure mages carry 2h sword or some other weapon around ?

From practical pov I feel like when fighting weak melee enemies the melee weapon can be a huge asset. Happened to me just a moment ago when I was fighting mage boss at the end of one dung ... failed like 5 times with pure magic just to give up and pick up an axe that was lying around and with it it was an easy job.

That light is strong enough to blind and repel servants of Sauron and worshipers of Melkor. Gandalf can also summon lightning, fire, create force fields and blasts that can destroy legions of enemies (much larger and stronger than the on the bridge of khazad-dum).