Can't give specific recommendations but some general advice.
I would recommend at least 4 GB of RAM. Any less and it will struggle to run multiple programs at once. For example Word open to write an essay, Firefox with several tabs for research, and a music player.
It's got to be a full-size keyboard IMHO. If you measure from the centre of the Q to the centre of the P that's 17.2 cm. If it's smaller, even if it's something like 95% normal size, that just ruins touch-typing. (I got caught out by that on a Bluetooth keyboard I bought recentl). If you'll be shopping with DD, go to PC World and let her try out the keyboards on the display models; it's one of the things you can quite easily judge.
Doesn't need to be too large. I'd say 12-14 inch screen is reasonable. Smaller and they start to put in the not-full-size keyboards I mentioned, bigger is just kind of unnecessary.
For your price you'll see two options for storage: eMMC which is a memory chip, and regular hard drives. Unless DD is doing photography or film courses I think I'd prefer the eMMC, it's faster so the computer and programs start up quicker, even though you get a lot less storage.
If you get your new computer and it's slow as snot, it might be unnecessary antivirus software preinstalled. Windows 10 has its own antivirus so the likes of Norton and McAffee can be removed. That made a big difference to our Dell.
Touchscreen is nice to have but you might not get it in budget.
Encourage DD to treat the laptop with care. Cheap laptops aren't always as robust as better ones.
A 'forever' copy of Microsoft Office is not included and will be required for schoolwork. Some laptops come with a 1-year free subscription but after that you'll have to pay.
If you want something very cheap that's not awful, consider www.getonlineathome.org/ . But I think DD might be disappointed by a second-hand computer.