Order means you have to start (and thus finish) DS9 before Voyager. That's a downgrade.
Also I'm always at a bit of a problem when it comes to recommending Trek to newbies because I so desperately want to tell people to give most of the first two seasons of TNG a pass, but I'm never sure if doing that will irreparably screw them over. having probably seen every TNG episode at least 6 or 7 times in my life (and many of them more than that) I have a hard time recalling how much understanding of the show the average person can start with via pop-cultural osmosis and how much they would need to absorb in seasons 1 (guhhhhh) and 2 (less guh, but still.)
Maybe it's more valuable to make a short list of <15 or so episodes from the first two seasons combined that
are worth watching so you can avoid cringey bullcrap like Code of Honor that one with the Space-Irish, Code of Honor, Angel One, Code of Honor, The Outrageous Okana (excepting the bit with Joe Piscopo simply because it's fun in a totally ironic way now. **** the rest of the episode though for wasting Billy Campbell as the worst knockoff Han Solo/Harry Mudd ever.), and Code of Honor.
DS9 has a similar problem, but the truly horrendous episodes are fewer and the show needs more of its build-up. TNG's far more episodic and far less interpersonal nature make it easier to skip stuff, and quite honestly more of season 1 is irredeemably awful.
EDIT: Oh, jesus. I was going to remark that at least the early TNG seasons avoided the frustrating "whiny/*****y Troi" plots, but I had totally forgotten that season 2 started with The Child.