I use JuMP as modeling language. For MILP i am usually using Gurobi or SCIP. For ILP problems have have been looking in to the exact solver https://gitlab.com/JoD/exact which seems quiet promising.
My experience so far: Quiet good at finding feasible solutions when constraints are complex. Really young code with a lot of potential. Not that good at finding optimas.
For NLP i usually go with either https://worhp.de/ or just IpOpt.