How can I make an interesting warrior type character? I've used magic in so many of builds and I'm getting bored of it. I hate stealth in this game too. I was thinking of trying to make a slightly weird warrior/rogue like character who focuses on the speed of attacks instead of power, but how would I go about doing it? Any other ideas are welcome too. I want to make a warrior-based character, but not have him be generic.

I don't know, make yourself a story, give yourself a background.

Well, find which warrior skills you prefer. One handed, two handed? Axe, sword, mace? Do you want to use a shield? Archery is needed IMO, especially if doing the MQ. You'll need some way to damage an airborne dragon.
Then just play.
I find pure warriors amazingly fun. My current Character is a warrior. She uses all warrior skills. She wears light armor and sword and board when travelling Skyrim. Heavy Armor and two handed when going dungeon diving. She always has her bow ready to damage foes from a distance.
Her three secondary skills are smithing, Alchemy, and enchanting respectively. She uses no magic whatsoever. She has a decent sneak skill, but doesn't rely on it.
She seems to be a pretty good build at level 27. The only thing is both armor skills are barely at 35. But that's because I avoid getting hit when fighting foes and don't care for training. I like to earn each level up.

That part is easy, but I was more referring to game-play itself. I like limiting myself to very specific weapons usually, rather than just having a mage who wields all types of magic or a warrior who wields any weaponry in this case. I was thinking of trying to create a speed warrior, if that makes sense. Like, he focuses on being quick and nimble in battle, rather than powerful. Is this possible?

I have a warrior thief type character. Light armor and dual axes. No potions and no magic.

Quite fun.

Yes. I know they can be fun. I like the idea of a speed warrior, if that makes sense. Like, focusing on speed rather than power. Not sure of the proper RP name for it. Does anyone? Is it really possible in Skyrim though?

use 2 handed weapons and clothing/no armor/very light armor(fur, hide)

basically the glass canon, these builds can be extremely challenging at low lvls but are actually really fun to play, you learn to rely on strategy rather than just brute force

Just start a new game with a dummy character and try to different combinations of the warrior skills. You'll have to try them to know what will work for you.

I am interested in playing as a Bosmer. What canonically fits them?

Always either write down a little backstory. Also I usually don't go with the set normal warrior style. I use One Handed, Light Armor, Block, and Archery. As my main combat skills and dabble in a little magic and alchemy later for fun.

Bosmer are known to be master Archers. They would shoot arrows from the treetops in Valenwood. They are also very agile. Better for stealth, TBH. But it could work for whatever you want.