In short: yes, you can pick it up at pretty much any point and most things you need to know will get explained as you go along. But by 'season one' do you mean the one from 1960s or from the 2000s?

I started with 2005 series, it took 6 episodes to properly hook me, but I've loved it since then... it's worth sticking out S1 for the change to David Tennant (Tenth Dr). I've gone back and I appreciate Nine a lot more now, and there really is a lot of back story you'll miss if you skip the first series. Just remember that it's 20y.o and never had the budget that Star Trek did. Once you've fallen in love and caught up with the Doctor, go back to season 1 from 1963 😉

If you want to jump in for an episode that might hook you watch the season 3 episode 10 Blink. I have gotten a couple friends hooked with that one. Then they went back and played catch up.

Season 1 of the 90s season does have a spoof of 90s reality tv that is Gold! Big Brother and The Weakest Link among others. I recently had surgery and rewatched it all during recovery. David Tennant is my favorite doctor, he starts Season 3.