This has probably been the theme so far that has made me think the most. Not to find songs per se, but what is it that makes a good opening song work.
I have split mine into 3 main categories.
An 'abstract' introduction. The one I already mentioned, not always a conventional song as such, but sets the mood. A song you Could do without, but would rather not. On its own though, not much. Tautou being one I already mentioned. Idles' MTT420 RR is probably another one, excellent build-up song to gateway into a hectic album, but on its own or as part of a playlist (like here for example), might feel a bit odd. Or Frightened Rabbit's Death Dream, a song that shocks straight to the point and launches you into the album, but not one you would choose to listen to on its own.
The big opener. Your best song first, open with the strongest of the album. I always consider that a bit of a cop-out tbh, maybe too obvious. Like Jimmy Eat World opening Bleed American, with Bleed American. Placebo opening Loud Like Love with Loud Like Love etc.
The debut. Bands only get one shot at this. Ever. Their first song of their first album, that people will be hearing for the first time and might stick with them as the sound or moment they'll remember forever. Like Placebo's Come Home, Brand New's Shower Scene, Audioslave's Cochise etc.
What to put forward? Fuck knows yet, I'm just havering. But then this thread is as much about the discussion as it is about listening to songs, so that's ok I guess.
Might try do one from each category, for the three songs.
Edit. Side challenge, is there a song out there that fits all 3?