Most bigger punches with not that much detailing, should work. I use nothing below 160gr and mine punch thru them. It's the thin papers that give me problems. The detailed punches wont work as they too fine but the basic shapes should be ok.
We have the Carl and Fiskars punches here and also the EK Success Whale punches along with some other store brand punches. Me mum is a punch fanatic and will create just about anything with them.
When not sure, go for the die cutting machines to be on the safe side.