Do I have to buy a new 64 bit version of Microsoft Office suite to work with my new computer?

Older versions or Microsoft Office are not compatible with macOS Catalina (which is what is currently installed on new Macs).

See the following for options:

If you have an early version of Office for Mac 2016, you can update it at no charge. However note that connecting to Microsoft 365 services using Office 2016 for Mac is not supported by Microsoft after October 13, 2020. See: https://docs.microsoft.com/en-us/office365/troubleshoot/administration/office-2016-for-mac-64-bit-upgrade

If you have Office for Mac 2011 or earlier (or don't have any version of Office), you can either subscribe to Microsoft 365 or you can make a one-time purchase. See: https://products.office.com/en-us/buy/compare-microsoft-office-products-for-mac?ms.officeurl=mac-compare-redir

Or use the free Microsoft Office on the web: https://products.office.com/en-us/free-office-online-for-the-web

Or Google Docs: https://www.google.com/docs/about/

Other options include using the free and very good Libre Office https://www.libreoffice.org/

or Apple's Pages and Numbers