I don't know what's generally available in Japan, but Kodak Carousels are plentiful, durable, work very nicely, can still be repaired and the trays are easy to find. I got my pair from a thrift shop and an estate sale, but there's always eBay. I don't know if there's a limit to how long you can leave an image up, but there's an air-cooling system blowing on the slide, so it's several minutes at least. Look for machine from the late 70's onward because these will have the modern halogen bulbs.
The professional-grade models are called Ektagraphics and they are supposedly more durable than the consumer-grade Carousels, but the differences seem slight. Ektagraphics might tend to have suffered more from rugged institutional use while Carousels have probably spent most of the last 20-40 years in a closet. I have one of each type and an important difference is that the Ektagraphic lens can be taken apart for cleaning while the Carousel lens is permanently glued together. As far as I know, the lenses are all interchangeable and for details there's plenty of info online from Kodak.
For viewing, any flat matte-white wall surface will do, but if you want to look for a portable projection screen, I like the glass-bead type better than the lenticular ones.