Not sure how cheap you need to go but a new set of Kenda tires are pretty cheap. A new set for my GS750 was $120 shipped for the pair. I put the same Kenda challengers on my RD350LC about 3 years ago. Haven't had any problems, they are wearing well and seem to stick well through the twisties.
I don't usually ride in the rain so I can't attest to their wet performance but there dry performance seems excellent for the price...
I and many others can attest to the wet performance of Kenda Challengers in one word: SUCKS. Other suitable words might include: death, maimed, slide, slippery, greasy, dismemberment, lowside, fear, fright, scary, and nope.
To be honest, they ain't so hot in the dry, either. There are many far better options nowadays.
If you need to save a few bucks, order up a set of Shinkos (230 or 712, depending on what fits your bike). They work great in the wet or the dry.