Here's my list of must haves:
Organizing bins- All sizes. I use mine for book bins, holding extra school supplies until we need them, and organizing classroom games. These are a few I use.
Drawer Unit- I bought mine at a garage sale and bought the tubs to go inside at IKEA. This is a pricier item but well worth the money. There is a tub for each subject and a few extra for things like notebooks, lined paper and chargers.
Another option is a drawer system like this. These work too but aren't as sturdy or as big.
Baskets- These will be used for everything from turn in baskets to organization for you. It helps to have a basket for each subject but if you're like me you don't have room for that so I keep one on a cabinet for turning in and one in my writing center to hold extra lined paper.
Buckets- I use three on my desk to hold pencils, pens and markers, sticks for calling from and one with quick brain breaks. I also use them as a sharp and dull bucket for pencils and to hold editing tools for writing. They don't take up too much space and make materials easier to find. You can get these in the dollar section at Target.
Pocket Charts- I use mine for calendar and vocabulary. Check your classroom before you buy as you might have one in your room but it takes away time and makes materials last longer when you don't have to staple and unstaple each time you use them.
White Board Markers- I thought I bought an excessive amount at the beginning of the year and I'm already almost out. Our school provides these but not the amount we need and not in colors. This is something to look into at your school.
Pencils and Big Erasers- These are very inexpensive at back to school time but we go through them like crazy. I had hundreds before school but they seem to disappear.
Blue Painters Tape- It's really good for holding things up for long term but doesn't leave a sticky residue. One or two rolls goes a long ways.
Clothespins and Popsicle Sticks- I use clothespins in a bucket and click them to the side as I call names. I also use them to show where students are in the writing process. They clip their name as they go. I've seen teachers who have students clip their paper with their name as they turn it in. Sticks can be used for anything. I use them for brain breaks, random pairing, and math facts.
Things to Pass On
Cutesy things- Although they seem like they'll be great, I never find time to get them out or put them up. This includes decorations, posters and big displays for student work. You'll have plenty of times to display work, it isn't necessary to make a big space of it.
Many School Supplies- I bought TONS of markers, crayons, and colored pencils before school started. Some of them I've used but a lot of them I will still have next year. I'd say a few of each is good but it isn't necessary to buy a class set or even enough for every other student. We have used classroom supplies and so far everything has lasted.
Seasonal Boarders- I never have time to change my boards for every season. I bought seasonal boarders thinking they would be great to change around but I haven't changed them once. Wish I'd just bought a few I liked and left the rest at the store.
Stickers, Pencils and Other Prizes- Although the students like them, they forget about them in a day or two and they add up quickly. I give pencils on rare occasions for great work like 100% on a difficult quiz or extreme effort. I've found drawing a star on students papers has the same effect as stickers but they don't end up all over the room. Also few things are as appreciated like a quick note. Anytime I write a note to a student it is treasured a whole lot longer than the pencil I gave them. Save your money for other things.
Cheap Bulletin Board Letters- Although the ones at DollarTree and other dollar stores are inexpensive, you get what you pay for, they fall apart and rip easily. I ended up investing in a better quality at a teacher's supply store and bought a couple of packages. I used the same lettering all over my room. It's more uniform and they last a lot longer. I've taken them down and put them up other places several times and they're still holding on. I think I'll be able to use them year after year.
Not Necessary but Helpful
Fabric for bulletin boards- It lasts longer than paper and you don't see the staple holes. I bought a few colors that could go with any theme and I have yet to change it. It's still holding up. Cheap fabric works fine.
Rugs and Chairs- I bought these for my library as I went. The rug was a steal from IKEA's as is section. It was a display rug and only cost $10. I bought the chairs at a thrift store by my house. I wouldn't spend a lot on these types of things. They get A LOT of wear. I also got some cheap pillows and pillow cases at IKEA. These make our reading time more relaxing.
Lamps and Picture Frames- I turn on a few lamps when we read or need to calm down. It makes for a less stressful environment when things are difficult. I bought a few picture frames and put pictures of my family and friends around the room. These make my day a little brighter. I also bought a frame for our staff picture, the kids love to look at the teachers pictures.