How can I create a custom organisation field with several entries available in a drop down menu which the user can select from?
Go to your Account Settings » Data Fields. Create a new field on the org and choose either the 'single-option' or 'multi-option' field type (depending on whether you want people to pick one or multiple options). From there, you can set up the options you'd like to let people choose from.
I have more tips on using custom fields in this video: