Some love, some hate it, and some just think it's ok
I'm glad you're watching through it again. I would focus on catching up with the new series while sampling the old show. While there's a lot to see that's good, you don't have unlimited time. I think you can get by with the netflix collection for the most part. As long as you watch an entire serial, you can pretty much watch them in any order. I'd probably start with a Tom Baker one because he's probably the most famous. Pyramids of Mars, Robots of Death, Genesis of the Daleks, The Face of Evil, The Talons of Weng-Chiang, The City of Death, and The Deadly Assassin are probably the ones I'd recommend from him.
For better understanding New Who continuity, I'd definitely suggest watching Genesis of the Daleks, certainly before Series 4, but probably before the first series with Tennant just so you can be introduced to Sarah Jane Smith. It's about three hours (six episodes), so it's a bit slower. BBC America did The Doctor Revisited episodes and they're probably good for an intro to each Doctor: The Aztecs, The Tomb of the Cybermen, Spearhead from Space, Pyramids of Mars, The Caves of Androzani, Vengeance on Varos, Remembrance of the Daleks, and the Doctor Who Movie. There are certainly other suggestions, but that's a good list. Maybe one episode with Time Lords would be appropriate (perhaps War Games), but that's about it.