Browse the wikis a bit and find a doctor you like. Watch some episodes from that Doctor until you’re bored. Repeat. You can watch them in any order you like.

Starting with the 2005 reboot is probably easiest and most accessible. Watch for callbacks to previous adventures. If those stories sound interesting dive into the back story.

Everybody has their favorite Doctor. Some like the leather clad skinhead. Some like the guy with the scarf and the Jelly Babies. Some weirdos like the guy with the celery stalk in his pocket. My favorite is the first Doctor. He’s in black and white, he’s witty, he’s grumpy and sometimes mean, and he lies. If you want to know about the origins of the Daleks you’ll need to find his episodes. The library is probably the best place to find these. I think there is always Doctor Who streaming or being broadcast somewhere at practically all times. I’m pretty sure I can search for Doctor Who on Plex and find some random episode streaming at any time.

As others have mentioned, several large chunks of the original series are missing, so be prepared for that disappointment.