I've heard a lot about the writing in this game which makes me interested in getting it, but I find the combat in some of the old IE games a bit tiresome (at least when it's put in contrast with say ToEE's combat, which is spectacular IMO)

So basically, how much of it is the game, and how easily can I avoid it?

How much combat there is depends a lot on your playstyle and the character you're RPing. Most fights are completely avoidable either through sneaking with a thief or dialogue.
If you're playing a stupid, non-sneaky fighter, though, there will be a lot of fights in the game.

How do I sneak though if the other characters aren't stealth characters?

Well typically in the parts where you can sneak through, you just need to retrieve an item, or pull a lever, all of which can just be accomplished by one character.

The first part of the game where sneaking is a recommended option, right after the thief NPC joins you, is a house filled with a bunch of brutes, whose leader owns a key to unlock the door to get out.
You can just waltz in, kill everyone, take the key off the leader's corpse and get out.
Or you can use the thief NPC (or the main character if you choose to make him a thief) to sneak past all the thugs, pickpocket the key off the leader, and unlock the door to let the rest of the group get out.

Which works just fine, until you realize that picking pockets automatically results in you popping out of stealth mode; also, at that point in the game, you'll be lucky if that character can make their way more than a few paces down a hallway before they fail their Hide check anyway.

Yeah, you can't really use stealth successfully in PS:T (and most of the IE games for that matter) without metagaming.

Also, some parts of the game are just simply littered with unnecessary trash mobs, like the respawning monsters in the catacombs, or the thugs that keep pestering you at every step in Sigil, but combat in the game is more of a nuisance than a challenge anyway. Whenever you're confronted in dialogue mode - which occurs often - you have the chance to resolve things using an alternate method to combat.

Hmm I remember using the sneak route successfully last time I played.
Of course I was using mods and one of those may have fixed the problems with sneaking. I agree with most of what you said, but if you really dislike the fighting in PS:T (and I agree most fights are pointless time wasters that detract from the rest of the game), you can avoid most fights.
For instance, you don't have to fight the thugs in Sigil. If you don't linger near them they probably won't go hostile int he first place, and they move slowly so you can just run past them if you want.
In effect, they're just there as a source of extra xp and money if you feel you need it.

Personally, I think the combat can be quite fun if handled correctly; if you fight by swarming your party toward a target, things *will* go badly due to the already problematic pathfinding AI running in fits and starts as they all try to stay out of each other's way. My advice would be to turn on the autopause for at least the end of a character's round, and use that time to coordinate the movements and actions of the party, plotting courses that keep the characters from bumping into each other and allowing them to get right next to their target before having them attack, maybe positioning a really good fighter in a position to where they can quickly turn around and start laying into another hostile once their target dies.