I know almost nothing of Stargate. Between the other two, I'd boil it down to: if you're more left-brained, watch Galactica, and if you're more right-brained, watch Who.

Which is not to say that the others don't have significant female characters with agency -- but Bechdel moments are few and far between on each because the women suffer from Smurfette Syndrome

Who or what is Bedchel and what is Smurfette Syndrome? Is that when there is only one female character?

BSG has the most significant female characters with agency.

Agency, yes, but there was also a tendency to sexualise them which SG1 avoids pretty largely with its main female characters. Sure, Sam's hot, but that's because she's awesome, not because she has sex or wears a slinky dress or any of that stuff.

I'll be the resident SG1 apologist--there's some crap there, but OMG, was it fun. They could be really funny, and they were pretty good and hamming up the angst. But never as unilaterally dark as BSG--if you don't know going it, it's horrendously bleak, and the finale made more than one person want to kill things.

Dr. Who is just fun. And easy to get through. You can watch SG1 forever, and then there's SGA off that.

Yeah -- a Smurfette is the Only Woman And She's Unbelievably Awesome.

From Wikipedia:

Bechdel test

This comic strip popularized what is now known as the Bechdel test, also known as the Bechdel/Wallace test, the Bechdel rule, or Bechdel's law. Bechdel credits her friend Liz Wallace for the test, which appears in a 1985 strip entitled "The Rule", in which a character says that she only watches a movie if it satisfies the following requirements:

1. It has to have at least two women in it,

2. Who talk to each other,

3. About something other than a man.[5][6]

A variant of the test, in which the two women must additionally be named characters, is also called the Mo Movie Measure. The name is a misnomer as neither Mo nor the other regular characters had been introduced yet at the time of this strip's publication.[7]

But never as unilaterally dark as BSG--if you don't know going it, it's horrendously bleak, and the finale made more than one person want to kill things.

Early BSG is less bleak. Yes, a near total genocide of humans at the beginning is less bleak than... season 3 had New Caprica, right?

I think Galactica is more likely to make you want to throw things at the end, and drink heavily throughout

I think Stargate is more likely to make you want to cheat and skip 3 seasons because there are so damn many.

I think Old Who is more likely to make you roll your eyes at the plots, effects, and costumes.

I think New Who is more likely to make you wish for the previous iteration of *[insert role in the show: Doctor, Companion]* and say, "Oh, not that villain AGAIN."

Any of them may make you want to smack characters for doing stupid things.

My recommendation would be Who, but that's me.

Early BSG is less bleak

This is totally a BSG definition of "less bleak." Doctor Who and SG1 have both cheerful and funny moments, never mind optimism for the fate of individual humans and the race in general.

I marathoned BSG once. Never again.

Battlestar Galactica, Doctor Who, or Stargate SG-1???

Have you seen Farscape? If not, it's worthy addition to the list.

t /not helping

Yeah, for a while I was okay with the bleak. But the end definitely made me want to throw things.

I think I've been very circumspect not suggesting Supernatural, but it's obviously the answer.