I'm a relatively new fan but I still began with the classic series. I first picked up my aunt's roommate's DVDs of "Spearhead from Space," "The Robots of Death," & the Key to Time box set back in 2004. It actually took me quite a while to get into the old series and it's usually very much an acquired taste. Between the slow pacing & sub-TOS production values, it's a tough sell for a modern viewer. And to be honest, had it not been for the new series, I doubt I would have spent so much time & money buying classic series DVDs and filling in the rich backstory of this franchise.
I suppose I go back & forth occasionally with my preferences. Currently, I give the new series a slight edge. Although, that may have something to do with the fact that I'm currently mired in JNT/Eric Saward crap during my effort to go through the series generally in chronological order. I might switch sides and start pulling for the classic series again once I cycle through and get back to the Hartnell, Troughton, Pertwee, & T. Baker years.
On the other hand, I've been pretty selective in my new series watching lately. I've been showing some episodes to my mother, so I've been very deliberately skipping over the crap episodes (and even some of the good episodes that I know she won't like because they're too sci-fi for her).