a non-conclusive list: tools, pants, dresses, socks, shirts, accessories, hats, gyroids, fossils, non-native fruit, native fruit, non-native perfect fruit, perfect native fruit, flowers, fish, furniture, wallpaper, carpet, bugs, shells......
essentially, any non-trash item (eg: anything you don't have to pay reese to get rid of!) can be on the premium board. there's no way to predict what will be on the board. it can be a specific item (eg: zebra turkeyfish), a category of items (eg: shirts), or a type of item (eg: sharks). i'd recommend keeping items which can sell for a lot more with premium on (expensive furniture, sharks, beetles and perfect fruit) if you have the patience, but it's often not worthwhile as it can take months!!