I suppose you have to balance accessibility, chronology/spoiler-prevention, and engineering the overall experience.
For example I've yet to watch TOS partly because I'm not sure I'd enjoy it after being spoiled by the production values of the later series (just as Star Trek spoiled my viewing experience of other popular sci-fi series, such as Farscape, B5, and Earth: Final Conflict because of Trek's--IMO--superior overall quality).
So I typically like saving the best for last; but that's a personal preference and may not be appropriate for everyone, especially as it would also mean subjecting an uninitiated and younger viewer to the worst/dullest parts of the franchise first.
With that in mind, showing TNG or VOY first might increase her chances of becoming a fan of the franchise. Sure, TNG covers some very complex and adult themes, but all of Trek does this except for the movies, and it's best to save the movies until you have some background on the Trek universe IMO.
I also wouldn't underestimate the intelligence of children. I find that grownups and even educators are frequently guilty of this, and when they sell children short, the child is either bored by the lack of intellectual stimulation, or it becomes a self-fulfilling prophecy.
As human-beings, we like being challenged, so letting her watch a program that may occasionally be beyond her grasp is OK. There are still plenty of episodes in every series that an 8-year-old can enjoy. It may even make her more precocious because she's used to entertainment with greater depth than kids programs. Besides, it's not like you're having her read The Sound and the Fury or Plato's The Republic.
Star Trek is also a pretty wholesome show. There's nothing in there that could really stunt or damage a child's psychological or moral development. In fact, it could very well make her more conscious of social & moral issues and become a better person. It'd definitely make her more of a free-thinker and encourage critical thinking at the very least, as well as instill a more inquisitive and rational mindset that'd make her more likely to question accepted societal assumptions and mainstream values than her peers.
While the Ferengi episodes of DS9 are some of the most generally humorous in Trek and also most accessible due to their much less cerebral nature, DS9 is fundamentally less Trek-y in spirit than any other part of the franchise. It's much less about exploration and more about war/politics/religion. It's also much closer to the "soft" sci-fi or sci-fi-fantasy end of the spectrum than the rest of Trek.
Plus, one of the greatest positive effects of Star Trek is the amount of scientists (especially in space-related fields) who were inspired to enter the sciences because they watched Star Trek in their childhood. If you'd like to inspire your daughter to go into the sciences, then again DS9 would be a poor choice, as even Enterprise does a better job of conveying the excitement and wonder of space exploration and the importance of science and technology than DS9.
So I'd personally show her TNG first to reel her in and also expose her to the humanist optimism/idealism of Star Trek. Then you can show her DS9 and VOY, ordered based on the relative importance you give to continuity versus quality & accessibility. Then she can watch ENT.
Then maybe when she gets older, she can decide to rewatch the Star Trek shows in order starting with TOS, which is basically my plan. This way, she's not going from ENT-era special effects and dialog to TOS.
