Fully Shrouded Toilet.

Easy enough but not quick enough for what you want to do or at least I wouldn't be doing it every time to refill. With old ones you just lift it off, with the push down flush button you have to unscrew it to lift off, too fiddly in my opinion to be doing it more than occasionally.
 
Don't know how good or expensive you have to go to get a push release type, mine is brand new and cost 300, maybe that's cheap I don't know, I was just looking for a particular type of bowl shape inside so that dictated my choice.