I am looking the simplest system that has both discontinous phase transition and a continous phase transition between the same phases (you can change one parameter).
discontinous transition: first order transition where (some) measurable has a discontinuity/non-analyticity as a function of (some) order parameter
continous transition: measurable is continous/analytical for all values of order parameter.
simplest: Requires the smallest number of mathematical symbols and is still defined exactly c.f. ising model.
EDIT: Removed water as an example. Above critical point, water has no phase transition as Alexei pointed out. So, all the transitions of water are first order...