Strip and re-paint or paint over?

I bought a completed 1/48 Airfix Buccaneer. It is pretty well built with photo etch in the cockpit etc., but I think I can give it a better paint job. Some of the decals flaked off in shipping so it really needs a re-finish no matter what. I will be sanding and filling some problem spots, but over-all it is well put together. In hind site it was a pretty good buy considering the amount of time it takes to get this kit to the painting stage. I have already removed the decals and washed most of what appears to have been pastel weathering off with warm soapy water. It was painted in a light coat of desert pink. It does not appear that any clear coats were used, judging primarily from the ease with which the decals were removed. The paint seems rather thin, one or two lite coats at the most. The panel lines are relatively free of paint given that the original maker accented the panel lines by actually scraping paint out of them to leave the original grey plasitic showing through. I intend to paint it in the over-all medium sea grey scheme seen during the Buccaneer's final years. My question is this: would you paint over the desert pink using it as a primer coat, or would you attempt to strip the original finish and then re-paint. The desert pink finish is reasonably smooth and, as I said, not too thick. My main concern is that the desert pink will show through or some how affect the color of the medium sea grey when painted over the desert pink. Perhaps a third option is to prime with light grey or white over the desert pink, but perhaps this step is unneccesary as the desert pink would provide a satisfactory base. Any advice is appreciated.