When you say the "copper is pretty corroded" that could mean a lot of things ... The copper coming out of the wall? Do you have copper supply lines from the angle stop (shut off valve) to the sink?
Pictures make all the difference.
Also, how handy DIY are you? If you are talking about drain piping under the sink, going from metal to plastic is a sure bet. You can buy cheap PVC (white) but the best is ABS (black).