I just want to play through this game and quickly and easily as possible. What would be my best choice of character/class to do this? Skills? I know some are better than others...

Choose or make a half-Ogre Melee type. Pick one of the auto leveling schemes and have at it.

i've been told magic is pretty easy too, but i haven't tried it. tech/firearms is definitely one of the harder ones, so don't do that.
the problem with a half-ogre is it's harder to find good armor, since most merchants don't sell large armor. but they have built in damage resistance. half-orc is a good alternative, but the low beauty and charisma will make it harder to get followers.

half-ogre is perfect for easy playthough. Just slash your way in.
Don't worry about armor or anything. You dont really need them when you are a Master in melee and dodge.
About magic:
It's easy in the way that it covers everything up:
Resurrection from the dead
Insta-kill
stat-boost
control enemy unit
teleportation
unlock a locked chest
ect...
by the way:
"as QUICKLY as possible"
ruining the game, are you?
as huge as this game is, it will not be so fast anyway

I would recommend a melee character with the Barbarian background.

Tech melee is pretty good. Once you get the pyrotechnic axe there aren't many enemies you can't kill (in 1 to 2 hits, usually), and it doesn't seem to take durability damage so you can bash golems, doors and chests with it.

How about pure mage with black necromancy and time magic? A lot of Willpower, a lot of Mana, Harm Spell and Time spells. You will be too fast for any enemies and kill them easly spamming Harm.

A mage with Force mastery or a melee specialist are probably best. I encourage you to experiment though, you shouldn't just try to complete it as quickly as possible. At least don't use a leveling scheme.

Two options for very easy playthroughs:

Melee Half-Ogre w/ Barbarian background, just hack and slash through absolutely everything. Full Dodge and Melee.

Elven Spellcaster with Dark Necromancy and, later, Chronomancy. Get Harm, Haste and the spell that slows enemies.

Either makes for an extremely easy playthrough.

Bonus of a stupid Half-Ogre with low intellect is that your dialogue options will be rubbish and you'll get to skimp out on a lot of quests, allowing you to "progress" quickly, I guess.

And do not forget about dog. If you want to win all fights very fast, you should have dog (DOOOOG!!!) in your party! :)

I prefer going with a human, no-background or hyperactive. Max Melee/Dodge/Dexterity to 20 quickly. Wander the wilderness or do the Tarant sewers to level up quickly.

Upping Dex gives you so many actions before anyone else it isn't funny. Make sure you do turn-based combat, and pick up training in melee/dodge as quickly as possible as well.

After that, pick what you want. You could migrate into thief, or pick up strength and some tech. Note: You won't be the smartest of the pack, but you can beat the hell out of almost anything before it can touch you. At level 20 I was clearing rooms of enemies before they had a chance to hit. Combat became quite boring throughout most of the game.

I have played the game many times and Half Ogre Melee with Magic (Harm and heal) ist by far the easiest combination I have ever had. Melee alone is enough to beat down most, and magic alone,too. Both together are unbeatable. But I do not recommend this, it is the only playthrough I abandoned halfway, there is just no fun, no accomplishment, no need to scour the land for items and xp, you can simply mow down anything.
For the first time maybe, but then maybe you will abandon the whole game because it sucks, so better just try magic or melee, not both,so you still want more.

i recomend taking your time with the game and going for the challenge. for me, a game thats too easy is no fun.