Translation:We would like to order drinks, please.
While beverage does mean drink, I don't know if I have ever heard anyone say "We would like to order beverages please." For language learning, it should be accepted, but unless you intentionally spoke with an upperclass, Mr. richpants, overly snooty British accent, I don't think you should use "We would like to order beverages please" when at a bar or restaurant. It just doesn't seem natural to me. Just my opinion though! Cheers!