dont buy new for cheap ....
I bought a cheap double pannier set made of plastic and they lasted 2 months
I have now bought Carradine Overlander panniers which seem to get good reviews. Hand made in the UK ....
I shopped around and managed to get these for £20 (used) off ebay and in very good condition ....
look for panniers made of canvas or similar if you want strength. They may not be 100% waterproof, but you can store your goods in plastic bags or large tupperware lidded containers, then pack them into your panniers