As tempting as it is to roll up your sleeves and put a desktop together, I wouldn’t recommend relying on one as your primary computer when you leave high school. You’ll want something to bring to class and study sessions, and you’ll find yourself spending a lot of time in libraries and coffee shops. And given just how cheap notebooks have gotten over the years, you really wouldn’t be saving much money by building a desktop.
The real question you should be asking yourself is what kind of laptop you need. We’ve listed a few in our back-to-school guide; personally, I’d recommend looking at Dell’s XPS 13 and the Surface Laptop. If you want to play some games, though, consider something with a dedicated graphics card, like the Dell G3 15 or Acer Nitro 5. Just be warned that you’ll be sacrificing portability and a lot of battery life if you go with a gaming machine.
You could also try and split up your budget. Get an affordable laptop, and then put the rest of your money towards building a desktop PC. You’ll certainly learn a lot by doing so, but be aware that these days you can also buy pre-configured desktops for less than individual components. Make sure you really want to put together your own machine before committing to it.