My favourite weapon is the Balanced Long Arming Sword. I'm primarily a melee fighter and I find that its balance of reach, speed, and power suits the way I fight very well.
My next favourite is the Balanced lance. I used to use the heavy lance because it had a longer reach but I've come to like the speed of the regular lance.
Favourite ranged weapon has to be the War Bow. Its a good weapon whether I'm on foot or mounted and has a great rate of fire for the damage it does.
Honourable mentions:
Siege Crossbow- I'm not a huge fan of crossbows but I find them better in sieges involving rhodocks or swadians as they don't drop any arrows for my war bow.
Balanced Pole Axe- On occasion when I'm fighting on foot I like to have a two handed weapon. I like this one because besides looking cool it levels up skill in polearms.
For my companions I just give them a heavy morningstar as the AI seems most competent with one handers.