I thought that "under construction" pages had been banished to the 1990s but I've noticed a few of them cropping up again. So I'm going to give the same advice that I and all the web gurus gave out in the 1990s.
Don't use under construction pages. It looks embarrassing!
I've noticed a few web designers have also started using a "being redesigned" page too. This is just as bad and just as pointless.
These sorts of pages are normally finished off with a little request to "check back soon". But nobody ever checks back soon. If parts of your site aren't up to date, people won't check back ever. It's better to have a site that looks smaller and only has a few pages, than one that has loads of unfinished pages.
The few times that I have "checked back soon" on sites that have "under construction" pages, the under construction label has never been removed and eventually the whole site ends up disappearing. I'm not the only person that has noticed this trend and people get a very bad first impression when they see these pages. People associate "under construction" pages with websites that never get off the ground and end up fading away (and the company usually going bust too).
Don't give people that impression. Just don't put anything up until you've finished it.
And anyway, your website is never finished because you should always be updating it anyway. So in theory, it's always under construction. An under construction label just means "too lazy to finish typing this bit up". And that's not an impression you want to give to your potential customers.