How can I backup only contacts?

By downloading a 3rd party app from AppStore, or by using this workaround:

Settings>[your name]>iCloud>Contacts (enabling that option, your contacts are synced to iCloud)

If you want to save them to your computer, I always use this procedure to keep all my contacts stored on an Excel file on my computer:

1.      Open iCloud.com on a computer's browser.

2.      Access with your credentials.

3.      Click on contacts, then on the setting's gear on bottom left side.

4.      Select all

5.      Export Vcard (.vcf file). If you choose "save" file, it goes among your “downloads” folder on your computer.

6.      Open this page:--> https://www.aconvert.com/document/vcf-to-xls/

7.      Select the vcf file to be converted, then you should obtain an ".xls" file.

8.      Click on that and you'll see all your contacts in Excel (you can save the file as .xls on your computer).

9.      Print, after adjusting the printing area.

Regards

Giulio