Question: I am setting up my personal website, and I have designed a simple "Coming Soon / Under Construction" page which basically has nothing but a small notice for the users. 

What kind of SEO can I make on this page such that it won't harm the full website's ranking later on?

Answer: 
Instead of a single "coming soon" or "under construction" line, expand it a little and explain *what* is coming soon and why a visitor should bookmark it or visit it again. 

There's also no reason why you can't already include a short about paragraph, some contact information and possible even a little subscribe function where people could enter their e-mail address to be notified when the site is done. Other than that, don't put in any unnecessary redirects or content that wouldn't be relevant to what would eventually be available on the site.
Make sure the content/keywords on the coming soon page is similar to the content that your final website will contain. Newer websites tend to get crawled less frequently so it may take a while to get your new website crawled and Google's index updated. So the snippet Google displays in their index may not be updated for a while after you launch your new site. You want to make sure it still jives with what your new sites has to offer.