I guess this means I've been living under a rock, but this hasn't been on my radar to watch at all yet. Are the first three pretty good? Are they adequately carrying on the legacy?
My background: I grew up watching TOS, was at first excited and then bored by TNG and the rest of the Berman series, and had my interest renewed by Abrams' films, which I believe are reviled primarily by Berman "endless meetings" era fans, and not first-run TOS fans. That said:
Star Trek Continues (TOS-C?) is, so far, surprisingly good. The sets, costumes, tools, and effects are easily equal to TOS Remastered. But besides that, the plots are interesting and after you get over different people playing the characters, it's like episodes of TOS that for some reason you hadn't seen yet.
Wife and I both loved them, and my 20 year old daughter, who grew up watching TOS Remastered, has given it her conditional seal of approval.
Something we all agree on is that there needs to be more episodes. Daughter holds back full approval only because there hasn't been enough so far to have an informed opinion.