When you're trying to analyse what specifically prevents you from getting to certain event, it's useful to read the walkthrough sort of backwards. You go to "Become best friends" event and see the requirements - 20 rp, Locker blowjob finished, "somebody used you at the library" conversation finished. Then you go to those events and see what requirements are for those events, for example Locker blowjob requires Drunk sex e t.c. And so on until you figure out what to do immediately.
Other than that, the events for each character are listed pretty much in the correct order, the exception major events that change your relationship level being at the end of the list.
As for sequence to get to day 9 - there's no correct one. You can try to use your time most effectively, in that case you should study in the morning in classes (and/or in the library or your room whenever you have nothing else to do), train with Jane at 17-18:00, start golden hands quest to get massage skill, don't forget to practice massage on Jane when she's watching TV. You might want to raise your confidence and fitness early in the game, since these are requirements for some quests to advance. You can pursue any girl you want at this point. Jane, Kara and Jess have almost no time-limited content. Joan has some time-limited content. If you don't ask for her first 2 selfies during first 9 days you miss them. I also recommend pursuing Joan first after day 10 to get her relationship to lovers before day 40.
. This does help me a lot.