How to run WordPress on a different port not visible to others – while tweaking

It sounds like you need a plugin to throw up a maintenance page, I like one called Site Maintenance.

You can install WordPress in it’s own directory off the root and then when the site is ready just “move” it to the root. If you try and have WordPress in the root along with an “Under Construction Soon” index.html file your index.php will not work. I prefer WordPress in it’s own directory as it keeps the root clean. “Moving” is only one or two files and a small database change – CAUTION – do things in the right order for “moving,” then just rename your old index.html to index-old.html and things should pick up and go – leaving you only 3 files in the root directory.

https://codex.www.ads-software.com/Moving_WordPress#Moving_WordPress_Within_Your_Site
or
https://codex.www.ads-software.com/Giving_WordPress_Its_Own_Directory

PS: You can also set your site to “Private”to keep search engines from crawling your test stuff – BUT – remember to un-check that box when you go live.