As Bob suggest, strip it. You'll be MUCH more satisfied with the results. IF it gets all the paint off after the 2nd (or even 3rd) pass using Peel-Away, you may only have to use steel wool on it.
Now, I don't know if you want the grain to be raised or not. If so, post up and maybe someone can tell you what to do. I don't know if the grain can/should-be raised if you're repainting. I know it can be done when staining.