Summertime Saga has a lot of interwoven story-lines and requirements for
passing those, so here's a list of things to do as soon as you can to
make these things a bit easier.
During Day 1 you'll make note of a master key and you'll find several
quests will require you to have it on order to finish them.

To
get the Master Key head into Mrs Smith's office on the 3rd floor at
school during the afternoon. Usually, her office will be empty and you
can go into her desk to get the key.
The computer in your room is broken and you'll mention this to Erik
at the end of Day 1. He'll tell you to buy parts for it at ConsumR at
the Mall. It will cost $200 but it's a good idea to do this ASAP.

Not
only does your computer allow you to train intelligence it's also
required to study for French Class as well as complete Jenny's
storyline.
Stats
can also lock you out of being able to complete a quest, so make sure
you've unlocked all the stat training possible by checking out our Stats page.
Working in Diane's garden is fine but you can make a lot more money delivering pizza once you have a bicycle.

Check
your mailbox to find the advert to unlock the Pizzeria and then save up
the $500 required to get the bike for much faster cash.