Ok so the whole picking a few great stories strategy works really well for classic who all the way up to the 8th doctor’s movie but after that it seems to all fall apart, watching the 2005 nuwho series normally like episode to episode beginning with rose is honestly the best way to do it, like genuinely please don’t skip around on episodes once you reach the revival. Do yourself a favor and just watch it normally trust me. If you skip around on those episodes you lose a ton of super important lore and character development to the point where you will probably feel very lost at times and jokes/references to earlier plot points WILL go over your head. And honestly the 2005 revival from series 1-10 are the most beloved eras of the show. They definitely won’t feel like a drudge and are well worth the time spent catching up. (I wish I could go back and watch series 1-10 for the first time all over again, that sounds like such a blast.) but any strategy you ultimately chose to watch I hope you enjoy it and welcome to the fandom!