I use CoverXP which have worked great for me the last some 3 years or so.
Start, load my coverprinting setting and then it's just to drag n' drop the covers and hit print.
When it comes to papers, I've used matte, semi-glossy and glossy standard photo papers. And they most often work like a charm. I do believe it's a matter of taste which kind you wanna use, I like mine glossy. Right now I've got some 180g/m² papers which honestly is too thick, so to give you a simple advice - try glossy photo paper somewhere between 120-150g/m². But perhaps you should wait for someone with a bit more experience to reply..