Can I put polyurethane on latex paint? I don't like the water based “varnishes.”
I'm not sure why you're putting a clear finish on top of paint. Typically that's not done except in special circumstances, like finishing a garage floor.
The only reason I can think of is the desire for added sheen. If this is the goal, your instincts are right: It's best to use a high-gloss oil-based paint (or solvent, as it's commonly known), which will give durability as well as the best sheen. If you use water-based paint, it's not as durable. It doesn't dry as hard.
As a rule of thumb, I only use water-based polyurethane on projects that won't have to endure much wear and tear, like interior door and window trim. But for any surface that requires durability - like kitchen cabinets that are constantly opened, closed, and handled - solvent-based is the way to go.