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?
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.
I don't bother with "coming soon" for a domain.
Search engines don't typically index coming soon pages, and even if they did, the coming soon page would only rank for the name of the website. No real progress on SEO can be made until there is actual content that contains keywords.
Putting keywords onto your coming soon page will just frustrate any visitors that you do get. Visitors like to see something they can use. If they got to your site and found "coming soon", they would hit the back button to Google and look for something else. Nothing kills your rankings and reputation with Google faster than being unable to satisfy visitors that Google sends your way.
The web is full of good intentions. Users have been trained to take any notices that something will be coming with a huge grain of salt. Users only care about what works for them right now. There is no way you can convince many people to bookmark something and come back later. There are only going to be at most a handful of visitors anyway.
Nothing on the web is ever "finished." All websites that want to remain relevant are adding new content and building out new features. Once your website has something on it that somebody can use, there is no place for "under construction" notices. They end up turning users away and distracting users from what you do have on your website that could work for them.
Just launch your first page. I'd recommend creating a simple "About Us" page.
This website is owned by X. X has the following credentials.
Just be aware that it probably isn't worth your time to create. It is really just for you.
If you've got Google Webmaster Tools setup and ready to go, create your sitemap.xml and submit your pages for indexing - they can show up in search results within minutes, not weeks.
It's important to be able to find your website, product or software without having to use the full domain as the Google search terms (e.g. www.mysoftware.com), so get indexed in Google as early as possible, even if that means you only target the name of your software and not the domain (e.g. mysoftware).
Hope this helps.