The main thing I remember from debate at University in the UK was that it was full of vaguely leftwing idpol types (so garden-variety US liberals I suppose) and that the debates themselves typically are supposed to appeal to morality. So make sure your arguments clearly describe how your proposed solutions are actually helping people/the world, and how your opponents are causing more problems?

For chuds, they'll typically propose something that's incredibly vulnerable to exploitation. So you can hit them with the old 'existing power structures mean that you're reinforcing the divide between rich and poor, by in practice restricting <x> to those who can afford it'. It's true for everything from anti-abortion laws to lax environmental regulations to poor worker protections.