The Galaxy S4 is a fantastic smartphone, but I can't recommend the 16GB version with such limited memory. Samsung is fixing the situation by rolling out an update to allow you to optimize your microSD card use.
I previously pointed out that the there were major limitationswith the 16GB Samsung Galaxy S4 since less than 10GB was available for apps and the microSD was irrelevant for apps. Thankfully, Samsung took it upon themselves to fix something Google broke and is reportedly issuing an update that enables moving apps to the microSD card.
Previous versions of Android had this capability, but that was changed in later versions (I believe it started with Ice Cream Sandwich). People who root and customize their phones can get this capability back, but the majority of people do not do this, so the number of apps they could install was restricted.
Some games today run 1 to 1.5GB in size so gamers were really feeling the pinch on the Galaxy S4. There are 32GB versions of the S4, but they are limited by carrier.