Let's hear what you found. You may be in Austrailia or England so share your short list.
Chromebooks don't run Office in your classic sense. From the web "Microsoft Office Online, the free cloud version of Office, is available as a series of apps for Chromebooks, and you can always use the native Google Drive to open and edit documents and spreadsheets."
So if you have a good internet connection you could try that out. Chromebooks are very cheap and my last 15 inch was a Groupon deal for under 89 bucks to my doorstop. If all you need is to write papers, why not go that cheep?
https://www.amazon.com/Best-Sellers-Computers-Accessories-Traditional-Laptop/zgbs/pc/13896615011 has a few sub 400 buck laptops but I'd skip the Chromebooks and HPs.
As to Office, why not Libre Office from Ninite.com if budget is an issue?
I need a new laptop for grad school. I only want to spend max $400. I really only need it for writing papers (with Microsoft Office) and doing research for class. I have heard about notebook laptops and Chromebooks but don't know much about them. I'd love some suggestions!