I wouldn't want a Robin Hood character to be some invisible superpower like some people are making him. The whole idea behind Robin Hood was the sense of danger because everyone knew he wasn't particularly strong, but he used what he had to his advantage, and was clever in how he used his modest skills. To me, making a super-powerful character with 100 sneak and 100 archery is massive overkill.
Robin Hood wasn't some super-powerful assassin, he was a noble thief, who preferred acting without too much bloodshed for the good of those less fortunate. At least, that's the image I have of him.
This is how I'd build him, but this would take a
long time because most of what he did wouldn't be centred around combat.
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He'd mostly do Delvin's jobs and Vex's burglary and sweep jobs. Other jobs would include delivery jobs for various NPCs, Find jobs (such as Kharjo's amulet, etc), and Clear jobs (such as the spiders in Shor's Stone's mine).
He'd probably use either a Forsworn or a Supple Ancient Nord Bow, with cheap arrows, and probably a Scimitar, all smithed to a
decent standard (like, superior or flawless) using looted smithing gear and bought/found smithing potions. Robin Hood wasn't a master craftsman, as far as I know.
In terms of armour, I'd be tempted to go with Thieves Guild set, although considering I wouldn't want to do much fighting I'd probably use this clothing item with Thieves Guild Boots and Gauntlets. For headgear I'd use either a green Cowl, or Linwe's Hood.
Strangely enough, I had a character running around in Linwe's Armour set already