moved out my parents' place last year into my own apartment with my girlfriend
a few things that have helped tremendously over the last year being here:
>buy an electric kettle if you don't have one for when you're short on time and want oatmeal, ramen, tea, instant coffee, cocoa, etc. without having to wait for a pot to boil or prefer using boiled water over microwave for certain food.
>if you have a thrift store/goodwill in town, check their furniture section. sometimes, goodwills especially, thrift stores get "corporate donations" from stores like target that include brand-new or like-new furniture (such as lamps, shelves, chairs) that were either under surplus or acceptable quality returns.
>use storage organizers like mad. if your bed frame is tall enough, under-bed bags (the non-vacuum ones) are cheap and can fit comforters, extra blankets, pillows, and more. buy racks for your cupboards to separate dishes or food and get more usable space. "furinno" brand on amazon is a good resource for decent budget shelves and other furniture if you don't mind the cheap looks.
>if you have an on-site laundry room and it requires quarters but there's no change machine on the premises, look for a couple reliable places to exchange for them as soon as possible. there may be times where you need to wash some clothes/towels at 11pm when most places are closed and you lack enough change to do a load or don't know of any alternative places when your usual place is closed/out of order.
Lots of good advice in this thread.
I would say it's good to have a first aid kit on hand so you don't have to go out to the store in case you cut yourself.
A flashlight or two for if the power goes out.
Also, packs of wet wipes are great for wiping down pretty much anything that's dusty or dirty.
Don't sweat the small stuff