Thickness Planer, Thickness Sander, or table sander?

I have a bunch of mahogany trim in my house that has been painted over the years by previous owners. I really want to restore this wood to its former glory. I'm just wondering what tool would work best.
I tried using some stripper product on some sample pieces but it doesn't really take the paint off as well as I hoped. So I've been thinking of using a thickness planer to just take a little material off. However, I've never used one and I'm not sure how rough this will turn out and if I'll have tons of sanding to do anyway? A thickness sander might work but I'm afraid it would take a lot of sanding for each board. It seams a table sander would have the same problem. Does anyone have any idea on this or experience doing the same?