What determines how much priority a move has? I had assumed it was based mainly on a move's strength, but, I saw in the smashworkshop that they said that priority is really weird in brawl, so I'm assuming there's more to it than just that.
wowwwww this is a fun question
Priority is about hitbox/hurtbox interactions. In general, if a hitbox hits your hurtbox you get hurt (and maybe go into hitlag and/or hitstun), so the relative sizes of hitboxes as well as the speed at which they come out as well as the same rates for your respective hurtboxes (since attacks tend to move your hurtboxes around funny) matter for the perception of priority. The speed at which your character's moving will also matter

(yay sonic lol)
More interesting are
hitbox vs. hitbox interactions. In Brawl there are several categories of moves that determine how these scenarios are resolved. If you get two Link Fsmash hitboxes to overlap before either Link's hurtbox was reached by the move, you'll notice it will "clash" (you'll see a little "clash bubble" appear somewhere in the interim space), and both Links will quickly
reset to a neutral state. Determining a priori which moves will clash against each other on which frames and whether or not one or both of the characters will reset (or proceed with their attack animation), and whether or not the hitbox will be
cancelled (if it is still able to damage the opponent) requires learning a crazy amount of nitpicky complications and exceptions.
Some guidelines:
Most aerials do not clash vs. other aerials; ex. Uairs vs. Dairs, it's just a matter of reaching the other's hurtbox first. If both reach, both get hurt lol.
Olimar's aerials
do clash, cuz they're pikmin lol, which are sort of like projectiles in some priority-ish sense. Except his Nair, which doesn't have pikmin lol.
Many specials (like Zelda's fireball) can clash against aerials; Sonic's Fair beats the fireball, for example. The aerial's hitbox will be cancelled, but in multi-hit moves (like Sonic's Fair, hence the example), follow-up hitboxes will still be able to damage the opponent.
Ground moves, in general, clash and reset both chars to neutral if the hitboxes would cause within 10% damage of each other, if they were to hit the opposing character.
If one ground hitbox does more than 10% damage than the other, the other will clash and the char will (probably, there are a few exceptions) reset to neutral, but the stronger-hitting char will continue through with their attack, probably thus hitting the opponent and damaging them (its hitbox is not cancelled) (you still might miss due to spacing or w/e, and the "reset" opponent can counterattack faster because their attack didn't follow-through any lol)
None of MK's ground moves clash against anything, except for his dash-attack. Funny tho, his Glide-attack
does clash against anything, even aerials. He has "transcendent priority" on his ground moves; it's basically the same as lasers that go through anything.
ROB's Fsmash, Ness' Fair, some of TLink's aerials, and a bunch of other random stuff has "transcendent priority" as well.
Wait, but how does Ness' Fair have transcendent priority? It's just an aerial that can't clash with anything, right? Wrong. Ness' Fair can't destroy Snake's mortar, which is one crazy-unique object in this game. Most aerials
can destroy the mortar. MK's can't lol. All of Sonic's can
MK's tornado has categorically different priority mechanics when it is on the ground, than when it's in the air. On the ground it can clash, in the air it cannot.
That's some random stuff off the top of my head. Hope it helps
