Fixie Vs Urban bike for small-distance commuting
For practical day to day commuting I would stay away from a fixie because:


You are not a very experienced cyclist, riding a fixie in traffic is actually not that easy.
No fenders, so dirty clothes/mud in the face on rainy days.
No rear-rack, so for luggage you are forced to use a backpack.


I also wouldn't go for the type of urban bike you link because: 


You will have a very straigth posture on the bike. This makes quick steering more difficult even though it might be a matter of life or death in traffic.
The straight-up posture with your pedals almost directly in line with your torso is not very comfortable when you have to put some effort into your cycling.
The small wheels make this type of bike unnecessarily unstable. 
A luggage rack on the handlebars leads to unpleasant/unresponsive handling.
It looks dorky (but that is just my opinion)).


I would find a nice secondhand bike that looks like the fixie you link but has fenders, a rear-rack and proper brakes.