I might opt that over Otter lake since you guys say otter is not so pretty
Well, the link of yours:
...Has a fairly typical picture of Otter Lakes. That is pretty much what it looks like, maybe a bit better at the larger lake. Like I said, Haystack is the reason. If you plan on climbing Haystack (an easy hike from Otter), it is the better choice.
To get to Branigan, I would take the trail out of Tiltill Valley, go around Mt. Gibson, and follow the ridge above Vernon Lake to the southwestern Branigan Lakes: from there the rest of the way is obvious and easy.
Thanks for the link. Nice pictures of Bearup Lake, Peninsula Lake, Inferno Lake etc.