To be honest with you I wouldn't bother with the sanding as it's not an area that is likely to get knocked and bumped so it's unlikly that the paint would get chipped off. Paint a small area with the paint you have chosen to see if it applies and dries okay looking but I think it'll be fine.
I would use some good quality oil-based paint like Farrow & Ball - I used it straight onto melamine panels in our old kitchen and it was fine - and if you take your time doing it you might get away with just one coat... If you do a small patch and it doesn't adhere well I would lightly sand first and then apply the paint. I wouldn't bother with primer or a second coat.