I remember Stadium 2 especially having some cute mini games like Rekoil mentioned. I can picture using the Cut HM to saw through trees on an assembly line with Scyther like a lumberjack. I remember doing pretty well with the spinning Hitmtop game too, and the counting one with the baby Pokemon. My personal favorite was Delibird's Delivery.
The games were kinda like the pokeathalon in HGSS with a little of the Poke Amie mini games, but a lot more of them in the Stadium games.
I'd love to be able to bring prizes back from a Stadium remake like decorations, ribbons, trophies and symbols into the Switch games. This goes without saying, but they must keep the mechanic of being able to transfer your own Pokemon into the Stadium and battle with them, while also having the rental Pokemon there, and let the rentals include mythicals again.