Good question! The Companions would be out anyway IMO thanks to their very strong Nordic feel.
I think you could probably forget about the big 4 factions: No Companions, no DB or TG, and no College.
The Civil War, you could I guess go with the Empire. But it doesn't feel like a very knightly questline IMO. I'd skip it.
That leaves the main quest and side quests. MQ could work; it's fairly heroic. But there are some parts where you're doing silly, non-knightly things. I'd see how far you can RP it, and quit when you feel like it. Opening up dragons is a good idea for this character, of course.
There are a lot of good knightly sidequests - especially in Solitude, so I'd make that your home. Elisif the Fair is a good patron/matron for you. Go to the Blue Palace and see what needs doing!
There are actually some Daedric quests that would work for this kind of character, I think. Without spoilers, I'd say Meridia for sure (just think of doing it on your own terms), Peryite perhaps (though I haven't done this yet myself - but think of it like you're interested in helping the afflicted, I guess), and there are a bunch of others that you could think of as
screwing over the Daedra. Go to Markarth, walk up the street to the right, and see what kind of trouble you can help out with

.
I had to adjust my paladin type character into a battered, grim paladin/mercenary. He was a good guy, but jaded. You might consider a similar approach in order to get through some of the quests offered by Skyrim.
Then, just by ruin-delving, you'll find lots of baddies to kill, and even some people to help. That's major spoiler territory, though, and anyway if you just consider yourself an adventuring, traveling, questing knight, that should give you plenty of reason to take detours into ruins for no other reason than that they're there.
Oh, hey, would you mind posting more details about your barbarian and witch doctor builds? Sound interesting.