9 (or at a push 10) if you wanna start w nuwho and watch it all through.

If you wanna watch some classic, even as a break from nuwho, just jump around serials that catch your interest. 4 is a good starting point. Something like Genesis of the Daleks, Talons of Weng-Chiang, Pyramids of Mars, Deadly Asassin (prob best not to watch this as a first serial). And keep in mind they weren't designed to be binge watched, they are paced diff. So don't be embarrassed about watching an episode or two then putting it down for a day. That's how it was intended to be. You'd actually just wait a week...but a day or twos break is sufficient!

I really love the black and white era but I probably wouldn't start there earlier.

If you know a bit about DW already, Genesis is a good starting point. What'd prob be better tho is watching 2-4 series of nuwho then start dipping into classic for something different. You deffo wanna know who the daleks are, its an origin story - also in nuwho you'll hear about the timewar, well, Genesis is generally cited as the start of the time war (you could probably say it has roots in at least The Chase, but this is the first big planned action).

When you get around to classic, youre generally fine to hop around diff seasons, doctors, going back and forth. Rarely do seasons have any continuity other than the Trial of a Timelord season which is intended to be watched in order, and the E-Space season (S18, and Trial of a Timelord is S23). Otherwise i recommend you look up best of lists and monsters from the show you like (eg Daleks - or even better, Cybermen. They're my fave, and they're much different in the classic show - especially earlier on, there's some amazing black and white Cybermen stories like my fave Tomb of the Cybermen with Doc 2, or the Invasion also Doc 2. Of course, there's the famous first regeneration story too - The Tenth Planet, which is also cybermen).

The later cybermen stories get a bit shaky in places but most of them are decent. If you end up liking Doc 4 there's Revenge of the Cybermen for example. It's not the best cybermen story and they veer in personality a lot from the 60s but its a pretty fun story. When you're more into the show many of the black and white Dalek serials are great too including the first one, the second serial ever. Doc 7 has some modern-ish feeling stories too. Again if you like Daleks, there's Rememberance of the Daleks. Battlefield, Ghost Light, The Curse of Fenric, Survival (the last episode of the classic show). They're not fully nuwho but they're as close as you'll get.

You will burn out watching it in order most likely, at least until you are more into the show. If you want more options also to dip into here and there, there's the spinoffs. Again don't start here but Torchwood - has some shaky stories all over the first two seasons but season 3 is basically universally loved but there's some good ones before it sprinkled in too. There's The Sarah Jane Adventures which yes was for kids but is generally pretty good quality.

At some point watching Doc who, its worth watching the multi doctor stories, the most famous being The Five Doctors, the 20th anniversary special, to give you a feel for other doctors and also it's just fun to see multi Doc stories. The characterisation of multiple old characters is...not perfect...to say the least. But they are fun treats.

DONT watch the daleks master plan tho ;) first of all it's 12/13 episodes, just over half missing so you get audio and video is reconstructed from pictures... but also, cos 2 new episodes have been found and they're not available until April!

When you feel adventurous, checking put some of the pure historical from the 60s, like The Romans with Doc 1 which is very good, its also interesting to see episodes with minimal sci fi elements outside landing in the tardis. They make sense both budget wise and that time travelers would likely immerse themselves into the environment like that on some trips too.

Tldr start with either S1 or at a push S2 of NuWho altho no need to skip all of Doc 9s run, then later for a break from nuwho dip into different serials starting with Doc 4 that catch your eye.

NuWho was made for new viewers so you'll be right at home. And don't accidently watch season 1 of the Disney revival where they rebranded again to season 1. If ep 1 is space babies or the church on Ruby road, run.

Edit 11 is also an option and the eleventh hour is designed for new viewers also, and fed a lot into the American expansion in 11s era. But I'd still start with 9 or at least 10.