Keyboard shortcuts have and will probably remain a main focus of action in high APM scenarios.
While we are not expected to be playing starcraft at 300+ APM, we can still benefit from some of the systems players utilize to reach such hights and aspire for improvements.
In this guide I will simply list suggestions of control options setup, explain why and finally provide some selfhelp material on how to gid gud.
I find that for a decent laptop + touchpad play experience, shortcuts help a lot!

To find the selection of control shortcuts in game menu, please refer to options/controls

What I am trying here is to apply is a simple WASD centered model known to FPS/MMORPG players which is easily adapted, efficient and enables quick switch to typing unlike utilizing a numlock combined with challenging to reach F1+ keys would.
There is no support and probably not a real need for going as far as RTS models go (such as detailed fleet interaction keyboard setup), however I did drop it in the ideas on G2G forum, and hopefully one day someone may mod them in or they will be implemented. (such a set of shortcuts would then only be enabled if you had a fleet selected and then something as a selecting a probe action could be much faster)
I suggest tweaks according to your own peripheral possibilities and thorougly encourage to go along with your personal preference, for instance if your mouse has 5 buttons, you should absolutely make use of them.
I find the biggest timesaver the end turn shortcut, while it can end up having you end the turn too hastily, there is no other button in game you click as often and the frequency only multiplies on slower speeds.So having that alone on your mouse can easily speed up the game remarkably while leaving the keyboard alone.

Here is the table of alternate keys going from top to bottom following the ingame control setup.
Most of them are self explanatory, but you can always check the detailed information over what each key does in game in mouseover tooltip:

There is little need to actually use the shortcuts, but if you want to strive to improve at something, it does not hurt to do so faster.
I am trying to pursue an approach under which every unnecesary mouse movement is a waste of time, and you can see for yourselves that my videos hardly reflect this as I am trying to make it easy to follow and the UI does not allow all that I would desire.
Optimally you should always be managing systems from empire screen, but then you can not observe the individual planet types that well and miss out on information. But it's a fair tradeoff for now having to browse around. Which can also be done by shortcuts utilizing the next and previous actions.