Ideally you don’t want to go too big as hamsters in strange situations will often prefer to be in a slightly smaller space but space is also likely to be at a premium at busier shows so the clubs usually suggest that larger cages are better off left at home.
When I entered the Pet Class with my Chinese I used a Medium Ferplast Aladino Carrier:
http://www.petsathome.com/shop/en/pets/aladino-carrier
It’s sold as being suitable for guinea pigs (it’s too small for a fully grown guinea pig) but it’s about the right size for a Syrian Hamster.
