I have watched Star Trek since I was 2 1/2 in 1972: my first memory of watching TV on a small B&W, memorable because I could not be unglued to come down for dinner with my grandmother. I don't think there is anything particularly special about being a fan for so long other than I remember what it what like when every subsequent series was new and how people felt about it.
I suspect that Discovery will end up being by third favorite Star Trek series, behind DS9 and TOS. The first season was rough, especially at the beginning. There are many bad Star Trek episodes, but I find Lethe to be outright annoying. I generally disliked the pacing of the episodes and the tone of the dialogue. However, I understood what the writers wanted to accomplish, and I found the season improved toward the end. I think season two is great: the Control wrap-around is shallow, but some many great things happen, notably the examination of sibling relationships, and two episodes are absolutely great, New Eden and If Memory Serves.
Do I mind the visual update? Do I care that the Klingons were redesigned? No. I thought it was strange back in 1979 when the Klingons and the Enterprise looked different, but I got over it. I don't like everything about the look. The Discovery bridge is too big, not necessarily as a reflection of the era but as a set piece. I could do without harsh white lights. The Discovery itself is rather nifty looking, although perhaps a big large. The Klingons are ok, although I hate the muddled speech patterns. The Pike-prise is awesome--I used to say that if I were a kid, I would love to play on the NX-01, but that was totally supplanted by the new 1701.
What does this old Trekkie think? I can't wait for season 3. I was anticipating it more than Picard. It's doing a great job of being a thoughtful adventure show which maybe could slow down a little. Sonequa Martin-Green is first rate, easily the best actress the franchise has had (it's to be seen if she can do better than that).