None of the day 1 options seem to matter much, except unlocking new CG's if you go to the brothel or peek inside the bathouse.

1.  Dead:  Peek at the adventurer's onsen
2.  Prisoner:  Work with Vanir.  Return to the mansion.  Accept their apologies, either before or after saying you're leaving.  Check on Megumin.  Any caress order otther than head, arms, legs, and breasts, then pretend to keep going.
3.  Victim:  Return to the mansion right away, then try the blinding plan.  Refusing here will advance the week, then you return.
4.  Rich:  Work with Vanir twice.
5.  Yunyun's lover:  Go to the lake.  Talk to Yunyun.  Invite her.  Tell her about your dispute.  Tell her you're hard.  A little, but I'm still hard.
Note:  Any choices after going to the lake other than the above will advance to the next week with you automatically returning to the mansion as if you had spent the week working with Vanir, then chose to return.
6.  Megumin's lover:  Work with Vanir.  Return to the mansion.  Accept their apologies, either before or after saying you're leaving.  Check on Megumin.
Caress her head, then arms, then legs, then breasts.
7.  Darkness's lover:  Work with Vanir.  Return to the mansion.  Accept their apologies, either before or after saying you're leaving.  Check on Darkness.  Try to be nice to her.
8.  Aqua's companion:  Work with Vanir.  Return to the mansion.  Accept their apologies, either before or after saying you're leaving.  Check on Aqua, don't tell them what happened.  Don't go to the fair until she agrees to show herself.
9.  New normal:  Work with Vanir.  Return to the mansion.  Say you're leaving.  Ignore them and leave.  Decide new rules.
10.  Supplier:  Work with Vanir.
11.  Darkness's master:  Work with Vanir.  Return to the mansion.  Accept their apologies, either before or after saying you're leaving.  Check on Darkness.  Give her what she wants.
12.  Starting over:  Work with Vanir.  Return to the mansion.  Say you're leaving.  Ignore them and leave.  Ignore them and leave again.
13.  Nursed:  Work with Vanir.  Return to the mansion.  Say you're leaving.  Tell them you can't control yourself.
14. Tolderable:  Work with Vanir.  Return to the mansion.  Say you're leaving.  Ignore them and leave.  Accept their conditions.
15.  LIfe as usual:  Work with Vanir.  Return to the mansion.  Accept their apologies, either before or after saying you're leaving.  Check on any girl, and follow any path not listed above, or continue without checking.