No one has mentioned this one yet, but it's pretty huge to me (eta, oh it was mentioned):
Bed. At the least a good mattress or comfy futon. We started out with my dad's (older than me so 19+) 3-4 inch futon mattress, on the floor. It was our bed for... 8 months, and we both had shoulder and back problems. We got a new mattress (it's still just on slats on the floor), and it saved our backs. We bought one that's 80% natural latex and no fireproofing for about 800 from ikea.
In my mind, a good sleeping surface is 100 times more important than a couch/chairs/table. We borrowed a card table, and are still borrowing folding chairs (we found a free wooden table by the dumpster a few months in. I was over the roof), and honestly, we have fun "picnic-ing" on the floor half the time, because the table is one of our few surfaces for putting things on.
A bookshelf, or several. We're bookies, so we have three half height bookshelves and they were filled in weeks. We could use 3 more.
A dish drain. People with dishwashers don't realize how indespensible these are (I didn't, until we picked one up at a garage sale).
Some of this stuff it depends on who you are, and what your starting out with. For us, a kettle would be nice, but a pot boils water too. I don't know that I would use a juice pitcher. Many bookshelves might not be needed for someone without so many books. For us, a couch/couchlike chairs will be a luxery someday in the future, but it's not a starting out necessity like a bed is. Since we love to cook we need (and have) a lot more cooking stuff than other folks. You could get by with a cast iron skillet, a 4-5 qt pot, a good chef's knife, a cutting board(bigger is better), a wooden spoon, and a can opener if you use cans.
Depending on the climate, a fan/space heater.
Honestly too, if he will have a little extra money to buy stuff, it's not the end of the world if he doesn't have everything he needs. We have had a lot of fun going out and getting stuff we needed. The dish drainer? huge excitement when we realized how much faster the dishes dried than laid on a towel. The mop? It was an excursion, fun to pick one out, SOOOO exciting to finally have a mop, AND a bonding moment with my grandfather, talking about finding enjoyment in simple things. The table that we found by the dumpster? I was giddy for a week. I was a GROWN UP with my own kitchen table. And a lovely (beat up, needing refinishing, cheap, wobbly little) one to boot.
I definitely agree about a rug and/or some art. Many many apartments are grey/white walls and grey carpet, and you can't paint. Having stuff on the walls and floor divides the space, makes it homey, and looks nice.
A houseplant. I recomend a spider plant. They aren't too big, they can take all sorts of light, they're really really easy to care for, and they are a particularly excellent house plant for improving air quality. A houseplant makes the apartment feel nicer, look nicer, smell nicer, and have better air.
Spices. At least the basics.
a few sponges, a dish brush a scrub brush.
hangers
a toothbrush holder and soap dispenser (and one for the kitchen!)