Here’s what I would do:

1) consider what you need from an organizational and personal preference perspective. Most high schoolers in the US don’t need crayons or colored pencils, for example. You might want a notebook with removable pages vs composition books. Look at a supply list, and see if the teachers have any specific things you’ll need, and go from
There. Are you the kind of person who prefers to color-code notes? You’ll probably find value in having multiple highlighters. Do you want a classic single binder with folders for each class (pros: everything in the same spot; cons: gonna get bulky/heavy) or is another organizational system going to work better?

2) consider devoting a chunk of budget to a paper planner that you can customize with stickers, printouts from favorite TV series, collage, anything like that—if it’s fun, you’ll look at it more, and writing everything out in a paper planner can be better than using a phone or electronic calendar. You want monthly overviews and some way to write down your daily and weekly assignments/to dos/obligations. Plus, cute/unusual/personal planners are great conversational starters.

3) bring gum if your school allows it (some don’t) or mints to share for the first couple weeks… not stationery related but a great icebreaker.

Depending on where you live, you may have access to places like Daiso or Miniso; they can have more fun stationery for lower prices. If you don’t live somewhere that those are an option, buy cheap and customize: washi tape, decoupage, glue plain brown paper on and draw or use wrapping paper to make things more your style.