It's 100% impossible for them to give me a series about adventures taking place between TOS episodes that I would find accurate enough, so nothing about that idea would interest me. A faithful post-TMP series is more plausible as those were movie-quality sets, but I seriously doubt it'll ever happen so I don't care about that idea either.
I can't think of a single remake I've ever enjoyed as much as the original and I'm at the point now where I pretty much skip all of them, so a TOS remake has basically no appeal to me. Would it make me upset though? If they said that time travel had erased the old continuity and this is what actually happened, then yeah I wouldn't like that at all. I give Trials and Tribble-ations a pass, but that's the limit. DON'T TAPE OVER MY TOS. If it's explicitly stated to be a Kelvin-style parallel timeline however, then fine, whatever. Maybe it'll get new viewers into Star Trek, maybe some good could come out of it. Either way I'll probably skip it.
To summarise:
New TOS adventures -

TOS remake -

TOS parallel universe -

Something new that builds on existing continuity -
Leave TOS to the novels and comics etc. in my opinion.