how-to: create new enfold site offline and then transfer to live & current domain

Dear friends,

I am quite new to this so please forgive my naiveté.

I have been maintaining pages, sliders etc. on our nonprofit meditation center’s current Etherna WP themed site. We would like to modernize / mobilize it and so have purchased the beautiful Enfold theme.

With help, we are recreating home and other pages, etc. that replicate but improve upon current structure.

Seeking suggestions how to rebuild offline and check that all is working fine and dandy before discontinuing current live site and publishing new site. (to same domain name: http://www.meditationinmass.org)

Can you steer me to documentation on how to do this with minimal affect on current site which we need to keep going?

I am not clear if creating “child theme” is way to go? Or, build a new site with new domain name (that’s private) that can be tested live and then switch out once complete and running smoothly? (will SEO’s remain or need redoing too?

Thank you for any and all help. Much appreciated!