Inexpensive is a relative term. Do you mean <$200, <$100, or <$75?
Also, are you building a new computer, or are you just upgrading your processor? If you are just upgrading your processor, then we need to know what your motherboard is.
I ran my Athlon 1.4GHz using 98SE back when that was my only computer for quite a while. I know PIII's run 98 very well too.
Someone suggested a K6...eh, they are fine but very slow when compared to other processors during that era...even Celerons! Unless you go with an Athlon or Duron, I'd stay away from older AMDs.