Apart from the animated series I've also seen everything at least once so far.
My first step into Star Trek was actually the first Kelvinverse movie which I watched some years after it had been in cinema, so around 2012 or 2013. At this time, I really liked it and also watched Into Darkness shortly after that, but then I started with the old movies and felt soon that this is "real" Star Trek if you will. I watched all of them until Star Trek VI.
Then I also started with the first season of TOS, I really liked it, but for some reason I didn't continue watching after the first three episodes or so. Then I also didn't deal anymore really with Star Trek for the next years, even though I had started to like it a lot, especially the classic stuff. When Star Trek Beyond was released, I watched it in cinema and liked it, but then I remembered also that the classic stuff interested me much more.
And then around september 2017, suddenly I felt the desire to go back to Star Trek. I don't know why exactly, I remember one evening I played Mass Effect: Andromeda and somehow it made me thinking of Star Trek again and that I actually still have a lot to discover there, plus I took up the contact again to one of my best friends I haven't seen for quite a time, him being a huge Trekkie who always told me about all the shows etc. At this time I started again with TOS and watched it all, then ENT, then TNG, then the first DSC season and finally DS9 and VOY. And in between also the remaining movies. It took me almost a year to get through it all, but I'm so glad that I took it upon me, because this restart was the time where my love for Star Trek really started to become strong.