Basically, a really simple and effective way to play the game is to always have an axe, a mace, and a good bow with you at all times. If you're dispatching some enemies while cutting trees or just want to live that viking fantasy, the axe will serve you well. The mace is a great weapon to cover whatever weaknesses your axe does not. Usually I will gravitate towards using the mace mostly because there are some very cool maces later on in the game, such as Frostner

People might try to dissuade you from using a battleaxe. They are relatively slow to use (dat windup on the first hit...) but can honestly be great fun, especially with the Crystal Battleaxe because you can actually parry attacks with a battleaxe and follow up quite easily. It is very satisfying and I would say try it out when you can.