As for the classic series on Netflix, "City of Death" (#14 on the Netflix collection list) would probably be the most enjoyable to a modern viewer. It also happens to be my favorite! It was written (or heavily re-written) by Douglas Adams around the same time that he did Hitchhiker's Guide (so the dialogue is fantastic) and features the most famous of the classic Doctors, Tom Baker. And a bunch of it was shot on location in Paris, so it doesn't feel as cheap as the classic series sometimes did. Oh, and the bad guy is played by Julian Glover of Indian Jones and the Last Crusade fame! Anyways, you can't go wrong with that one.
Also, #7 & #8 are both pretty good and feature Tom Baker's Doctor with Sarah Jane.