I think they should aim for the mid-1920s. That gives them enough space between the time period of the movie and the time period of TOD (1935) allowing audiences to more easily accept Indy looking a bit different, but it also doesn't go too far back, so we won't be stuck with a kid Indy. A 25 year old Indy could work okay.
As for the tv series... I just have a REALLY hard time accepting it as canon, and I would be completely fine with it being removed from canon in favor of movies that feel more Indy-like. Aside from his name, the character in the tv series was not Indiana Jones. He had a completely different personality/attitude (yeah, I know people change, but they don't change THAT much from their 20s to their 30s.)
Why would anyone want Indy to go beyond the 1960s? Do you really want to see Indy trapsing around in his fedora and leather jacket in the 1970s?
I totally agree with you that going into the 1970s would be a bad idea. That's one of my big problems with Harrison doing another Indy film. His age pretty much forces them to set the film in the 70s, and for me, the 70s isn't the time period I want to see when I watch an Indiana Jones movie.