Painting of Paneling

I can't really comment on the painting part. We're just now doing this ourselves for the first time in a rental house. HOWEVER, I can tell you from a previous home, that the sheetrock behind your paneling may very well be installed backwards. That is, inside out. Ours was, and from what I understand, this was/is a signal to the sheetrock finisher, and the painters, that the wall is getting paneling. Ours had a very rough tape and finish job on it and we had to have the entire surface skim coated. It was well worth it to get rid of the paneling. Keep in mind also, if you remove the paneling, you may have to retrim the doors and windows, and your switches and outlets may need attention also. depending on how far out the boxes are set.

Only if you pick colors of stain that clash.

If so, then painting the walls becomes

Not necessarily. See above.

A friend of mine did his panelling ( cheap kind of 1/4' plywood kind with grooves ) that was VERY well stuck with construction adhesive ( found by trying to remove one small inconspicuous piece. He used a product that came on a roll, that was pre pasted with an adhesive. Had a texture like muslin, and was applied hoizonatlly on the walls - kinda like wallpapering sideways. Once set up, he primed and painted, and you can't tell its not wallboard. Don't recall the name, but he got it from a paint-specific store maybe Sherwin Williams?