Um. It's not gonna work unless you have the watch brand it came with. Un-coded means un-standardized which means un-interchangeable.
As others have said, they all work IME. I've got a couple of really cheep ones and a polar one. They all talk to each other and to the equipment at the gym. The only one that they dont work with is concept2 rowers which for some reason went against what everyone else had done and use ant+.
As for the original question, I've not seen a standalone cheep 'watch'. My polar F7 was about £25, and my mum's got one from Tesco which works just as well, but both came with belts.