Probably should have done this earlier, but I'm still relatively new.
Been a Trek fan for 20 years now. I got into it mainly because I had just seen the Star Wars movies on USA Network for the first time and wanted to see more space adventures. The same network was airing THE MOTION PICTURE, so that was my first slice of Trek. After that, I got into the rest of the films, enjoyed them enough that my folks got all the six films on VHS for me. Funny thing is that I was completely unaware that there was a TV show with more adventures with Kirk and did not see an episode until August of 1994. It was "The Enterprise Incident", I remember that because the VCR had to be timed for past midnight and there was no other way of seeing the show on TV. It was pretty strange seeing the same crew, yet much younger and in a lower budget, but still fun.
Over the years since then, I didn't watch every episode of Trek religiously. I'd go see the TNG movies in theaters, even though I didn't see much of TNG until TNN started airing reruns in 2001. Same thing with DS9 once that aired in reruns in 2005, and then VOY in 2007. I did try to watch ENT when that started, but I didn't commit so I dropped out 8 episodes in. I wouldn't get to finally watch every single episode of every show until 2009 as I rented on Netflix. I'm glad I did, even if I thought VOY was mostly a waste.
Because of that experience, I always encourage anyone who wants to try out a franchise to watch everything if they can, rather than just ask others opinions on which bits to see. When I'm asked which Bond films to see, I'd tell them my favorites but ultimately encourage people to see them all to form their own opinions, because they might find something enjoyable in a movie I might not have cared for. Same with Trek. I don't care for VOY, but it does have its fans so I don't discourage anyone.