Office 2003 ought to run on Windows 10, though it is a few years since the last updates/fixes were issued. If you do install it, the patches should come down automatically from Windows Update.
Office now comes in three styles.
Office 2019 is the set of programs to install on your machine, in the way you have been used to. A one-time payment, with about a decade of updates/fixes. There are several, differently-priced options, containing assorted modules.
Office 365 (recently rebadged as Microsoft 365) is a version where you pay a subscription. Again, various prices depending on what you need to use. As long as you keep paying the sub, you get the latest updated versions. Not sure what happens if your cash runs out - probably something like not being able to save changes.
For either of these styles, educational versions are available, at lower cost. Pretty much any type of education entitles you to a (legal) discount to these and other stuff from Microsoft.
There's also Office Online, where you use the apps for free through a web browser. I understand that all your documents need to be stored in Microsoft's OneDrive. It might be OK if your internet speed is fast enough and your files fit in the space available.
Also consider the free options, such as LibreOffice and OpenOffice, which provide very similar features to the Microsoft offerings.
