I've always had a lot of trouble envisioning what a third TMNT series would be like, because it always winds up coming out too much like the 80s one or too much like the 2K3 one.
Like I would say, "Make it like Wolverine and the X-Men!" but...that's 2K3. They even have had some of the same crew members.
I guess I would make it kind of Spectacular Spider-Man or even The Batman-ish. Generally villain-of-the-day-ish, but with an overall arcing story as well, with as big of a rogues' gallery as possible, drawing on as many sources as possible - Mirage, the 80s cartoon, the Archie comics, the 2K3 cartoon - and all with total redesigns. I don't want to see just the same old villains brought back - I want them reimagined.
I don't want a straight adaptation of the Mirage comics, because that's why we have the Mirage comics

I like adaptations that build on what came before and make something entirely new out of it rather than just following by the letter.
And assuming the action could be rendered well enough I'd want it CGI this time. Not the same look as the 2007 movie but in that ballpark.
I couldn't care less what company made it, as long as it was done well.