Ah, your first house. Great adventures lie ahead.
Refurbishing existing cabinets can be fun, with a range of outcomes. My suggestion would be to take it one step at a time. Stripping the old paint, and learning about the range of chemical strippers available in the process, is the obvious first step. You could sand them down and repaint at that point. Simple and easy.
Adding detail, however, opens up other issues. After stripping, examine the construction of the doors carefully. Are they really "solid wood" (boards glued together at the edge to form the panels), or are they of a "solid wood" core with a veneer surface? The difference can effect what you do, and how it will look. Repainting simplifies things, compared to staining and varnishing, of course, as the paint will hide things like variations in the construction.
Changing the edge profile should be possible without changing the actual outside dimensions of the doors. Adding a detail to the face of the doors (such as making them appear to be frame-and-panel style), however, is more problematic, or at least potentially so. For example, routing a groove around the boundary may release internal stresses in the boards used to make the panel, which might cause the door to warp. Unfortunately, there is no way to know this in advance. So, it's good to have a back-up plan should the unexpected happen.
Have fun, and be safe.