How do I fill in the grooves in wood paneling in order to paint over it?
I might consider wallpaper as an option. You can surely find it in a plain paper, in your choice of colors, or any of a million patterns. First, you would need to fill in the grooves with spackle, but now you can do it very quickly. No worries there, just ensure that there are no voids behind the paper. And a plain paper would be relatively inexpensive.

Another choice is to use a product that is closer to a latex caulk to fill the grooves. It stays semi-flexible (so less fear of cracking) and is paintable, and you can buy it in a tub form to spread with a knife. I used a product from DAP (sold as a crack filler) once to solve a similar problem, filling cracks in a ceiling.

A third option is to buy battens - thin strips of wood moulding, perhaps 1/4 inch thick, and perhaps an inch wide. You can even choose the profile for the moulding if you wish to give it a custom look. Nail these vertically over the grooves, and paint it all. You might also paint the battens a different color to highlight them. This will give the wall a completely different look, rather than just looking like painted paneling, and no spackle will be required.