There are universal developers, but most folks use different developers for film and paper. They are similar enough that you can use one for the other, but you will likely not get optimal results. We use the same fixer for both but at different dilutions. I also think that is common. As for stop, it is exactly the same for both in our darkroom, again, I think that is the norm.
Wetting agent is not an absolute necessity, but if your results aren't what you want after drying your negs without it, you might consider getting some. If you get drip marks, etc, the judicious use of drying agent can help prevent them. Some folks use distilled water for their final rinse, and that can help as well.