Where should a champions health be depending on what role they're playing?

There is no specific requirement or cap for HP, it is completely situational.

If you die too quick, then build some resistance and HP. If you are ahead, feel free to spend gold on some damage.

It's entirely situational and depending on the champion. There's no specific answer for any specific role.

well in general: Tanks have the highest, then Bruisers, and Mage (APC) and Marksman (ADC) have about the same cause most don't build HP, but it's mostly situational and depends on what champion you play and are against.

I mean, like, with my Pantheon build, I have 3000 something hp, and it's below 3050. Is that reasonable, or should I reconsider some items?

bruisers tend to be in between 3k and 4k health (with a good amount of resists) at full build, depending on how many damage items they did or didn't build.

Marksmen are usually almost full glass cannon, so between 2k and 2.5k health is average.

Tanks can usually get to between 4.5k and 5k health, depending on how much resistance they build and if they have cinderhulk.

Mages like marksmen are usually near glass cannon, but they also often build things like RoA and Rylai's, so somewhere at or above 2.5K is average.

Supports (throwing this in because I can) are usually squishier than their lane counterparts, so a mage support usually has around 2k to 2.5k health, and a tank support usually has around 3k to 4k health, depending on how much gold they have and how much of that went into support items without tank stats.

For someone like Pantheon, who is a bruiser/assassin, something around 3k is average, since he likes being a damage threat but needs a bit of durability to not blow up.