1. Kitchen Basics: The important things that might top this list might be a can opener, sharp knife or wooden spoon. Check out this list at The Kitchn for more ideas on these essentials.
2. A Toolbox: You'll at least need a screwdriver (or two), a hammer, a tape measure, a level, adjustable wrench, and set of allen wrenches for all those IKEA purchases. The rest is up to you.
3. A Plant: Even if you kill it in a few months, the breath of life they bring to a space is unmistakable. If your thumb isn't exactly green, try a succulent that only has to be watered every few weeks.
4. Books: Even if you have a Kindle, a few books are always good to have around. Sometimes you just want to flip through the pages for inspiration or a little reading. If you're not big on collecting such things, make them classics that even a visitor might enjoy picking up.
5. Baking Soda & Vinegar: It doesn't matter what mess, mold, or grime the last tenant left, this combination of ingredients can clean just about anything. Save your money for other things like food and curtains to block out the view of your neighbor who refuses to wear a bath robe.
6. 3 Light Sources: Many apartments can feel lacking in light and often your first apartment isn't as awesome as you wanted it to be. Remember 3 light sources for your main room and it will always feel more like home. Plus, as a rule of thumb, all overhead lighting in apartments is ill-placed, too harsh, or too dim.
7. A Place To Lay Your Head: Yes it seems overly basic, but it's easy to get caught up in the smaller things you might need. Just because you think you can get away with sleeping on a futon doesn't mean your back will agree. Sleep comfortable and everything else, even the smallest space with the worst bathroom is suddenly tolerable.
8. 5 More Extension Cords Than You Think You Need: Unless you designed and built your own home, there's a 99% change your outlet ratio to products that require them will suck. Having a few extension cords or power bars on hand will save you frustration and trips to the hardware store later on.
9. A Box Knife: This small simple tool will save you a great deal of headache when it comes to opening moviing boxes, unpacking furniture or taking off zip ties held into new packaging that needs to be disassembled. You won't need it until you have no other choice but to go buy one and then you'll think back and say, "Apartment Therapy was right."
10. $50 Emergency Money: It doesn't matter if you keep it in the bank or stashed in your secret hiding spot, every first apartment has some sort of emergency. It might be the need to escape and have a night out, a lamp you didn't think you'd need or possibly a fan due to the lack of air circulation. Big or small, there will always be something.