Your quest for a less-than-$120 rod-reel-line combo is likely to come up short on one, if not all, of the three components. That being said, don't give up! Remember though that you're still going to need to buy some backing and butt and leader material to assemble your leader. How well you can cast with a low-end fly rod and fly line depends on your skill as a caster. I wouldn't hesitate to go check out Wal-Mart or Sears and see what they sell, but keep in mind that this may be stuff you throw away in a year or two, especially if you do much fishing.
As for flies, the good thing is that snook and redfish are not very particular--again, anything sold in big-box retail stores, if you can find it, will probably suite your short-term needs.