Personally, I think that I prefer 2D characters drawn by me, because they will look exactly like I want them to look. But I don't think that 2D BGs are as beautiful as pre-rendered ones. Here is where I need some information...
With paintshop, will I be able to add complex texture on my BGs? Also, what about light and shadows? Or animated scenes??? Can I add some flashing lights with sprites?
I know its kinda old, and you probably dont even care anymore.

I, myself, prefer 2D backgrounds. I never been a big fan of those 3d adventure games(well, alone in the dark doesnt count

), but its totaly up to you. Think I would have in mind if going for 3D pre-rendered ones is that your sprites might actually not fit on it at all, but then, Im not sure how you mean, you can use cellshading and all that to make it fit 2D more. You also ask about paintshop capabilites, I would say that it stops with the artist, its just a medium after all. Making beatliful 2D games is possible, with flashing lights, subeams going thru windows, and 2d characters casting shadows. You just need to be creative, you can paint the ligth on a new layer and use it as a sprite or such which you can switch on and off, etc.
Texture a background to death isnt such an good idea, the spites wont fit. It will make them look very flat since they will miss alot of details, and detailing 2D characters will only make it hard to animate.
You can study some games thats on the market and see how they solved problems that they might have.
here is a background of mine with 2D characters in it:

The background doesnt have much textures, but the sprites fits, and I think thats the important thing - making the whole game fit together.