TNG has aged the worst and would benefit the most.
I find all of this "product of it's time" stuff to be rather silly, and I feel the same way about the Star Wars special editions. As long as the actors performances and the stories being told (the only
things that are truly important and relevant) are unaffected, then I say go to town on the effects, as they are the least important and mosty irrelevant aspect of any good Trek anyway.
(And no, Greedo shooting first did less than nothing to either the story or Han Solo's character. How anyone can say that Han Solo loses any "edge" he might have had is beyond me, and I really think that such people who believe this need to watch it again. Han shoots a being in a public place and in front of dozens of witnesses. He then stares down the room, casually tosses the barkeep some coin, apologizes for the mess and strolls on out. And somehow he loses his edginess...?