the best solution to develop wp local and push stage ot production site

Probably best to familiarize yourself with Centmin Mod Nginx vhost site structure of where files are so you best know what needs backup/migrating or copying first. Then you'll know more about what and where files and data are first.

See official Centmin Mod config file outline at Centmin Mod Configuration Files - CentminMod.com LEMP Nginx web stack for CentOS and also check out below guides on normal manual site moving which outlines which of those files need to be backed up and transferred usually.

For moving site data there's 2 general guides where the principles & steps of backing up and moving data is the same just slightly different for

1. Moving Centmin Mod site data to another Centmin Mod server
2. Moving cPanel/WHM site data to Centmin Mod server

Those guides move alot more than just the site(s) in question but config files etc. You can use your own best judgement as to the config files and whether you want to move them or just use the fresh server setup Centmin Mod config files as they get auto optimised for the server Centmin Mod initially installed on.

If your old site isn't centmin mod or cpanel/whm based, then those guides won't be 100% applicable. But the general overview of what needs moving and where everything is structured in Centmin Mod LEMP environment is worth reading up on.