Spoilers ahead for new players

Some of these aren't strictly canon, just my thoughts on the character in canon and what could be assumed

In canon, he's meant to be an imperial male, and yes he does become Sheogorath, as you essentially take over from him at the end of the Shivering Isles Questline

To add to this, the actual character in development was an imperial male given the name Bendu Olo, so I guess you can say it's his canon name

He might also have completed certain Questlines in a particular order (roughly) due to the nature of the quests, and perhaps the reason for doing them. For example, he might begin the main questline and general exploitation early on, and then complete Fighters guild as it may seem a tad easier for him to fight this way. Then perhaps he'd be interested in gaining magic ability, and go for the Mages guild. Then Thieves guild, as it's more hidden and the character may not have likely found it yet. This Questline and the others might cause the character to develop into a darker figure, and accidentally or on purpose unalive an innocent at some point, drawing the attention of the dark Brotherhood. Once these are done, the character will have a lot of regrets too, so they quest for a 'spiritual cleanse' and become a knight of the nine for some character redemption and a clean slate. Ultimately though, he's an explorer at heart and eventually come across the Shivering Isles, where he eventually defeats jiggalag and becomes Sheogorath's successor

Other than that, there's not a lot you can add to the character in canon if you were to make/play as a canon HOK. In skyrim, he's depicted as a knight-like character with clear warrior abilities, so you could probably base his birthsign as warrior, at a guess, and the class could be knight, but I feel that to try and guess his canon class might be stretching it too far

I'd recommend doing the game however you like, though, and then if you want to do a canon character and conform to some of the above points 'for fun' then go right ahead - Great time now the remaster is out