Risa

Start with TNG. But the first two seasons are pretty bad. Watch the first episode where everyone gets introduced, then skip to s2. Tasha will be gone and Worf will have taken her place. Riker will have a beard. The whole show will be much better. You can look up which episode Riker grows the beard. The entire show becomes way better from that point forward, so much so that "Riker's Beard" has become an expression which means the opposite of Jumped the Shark. You can go back and watch the first two seasons when you're done if you want to. There are 3 really bad episodes during season 7, but the finale is amazing.

When you're finished, watch the first episode of DS9. You'll be super bored. Then skip to the one where Miles becomes a prisoner. Then skip to middle of season 2. It doesn't really pick up until the beginning of s3, but there's some important developments during s2 that you'll want to catch. You can loop back around at the end if you want and watch the first 2.5 seasons.

From there you can go back and watch the ToS if you want, but it's pretty campy by today's standards. There's a few exceptional episodes, but even those are just okay compared to the 90's stuff. There are a few TNG movies too which are okay. Once you're done with TNG and DS9, you're on your own. I don't really consider anything except the first three series to be valid Trek.