The word "paneling" covers a wide range of products. On the bottom, you have cheap plywood with a picture of wood or something on it. This stuff is similar to ready-to-assemble furniture and it is hard to get paint to stick to the mylar that the picture of wood is printed on. Prices start at about $3.50 a sheet for this kind.
At the top end you have some very expensive plywood vaneers that are then finished at the factory. The plywood is much thicker. This can easily be painted unless you have a "wormy" wood look or something but usually the wood is so beautiful that you don't want to. Prices for this type are in the $50 a sheet and up category.
There are a multitude of variations in between. With this wide variation, you really can't say that you should always refinish "paneling" the same way or what the results will be. You really need more information to make a decision.