So... I want him to be a sort of wandering adventurer (thus no buying a house).
I'm thinking something like 1H+block, smithing, light armor... maybe archery?
what quests should I do?
Companions seems not very wander-y since it's a brotherhood after all.
Bounty quests seem nice though... Any ideas?

Travel from town to town, accepting all kinds of misc. quests that you catch wind of. Go to the inns frequently, talk to everyone you can before you leave. Other than that, explore, and explore some more.

Try staves with a one handed sword.