Inf you go for Integer based algorithmic I recommend you stick to 32 bit Integers since most modern CPU's work either with 32 bit or 64 bit registers when doing math. This way you avoid converting from 16 to 32 bit and back all the time. Not to mention that integer overflow Flags will work as they should. Not sure if they would work on modern CPU's when using 16 bit integers unless you mess with FPU parameters which could lead to host of other problems since on modern computers no application gets exclusive access to specific core. Therefore changing FPU parameters might affect other applications.
Any way many games actually rely on Integer based physics. Some even using 64 bit integers to achieve high enough precision. And there are whole libraries for doing Integer based math that you can find on internet.
Another big advantage of using integer math is that if you are serializing and deserialzing your data to to some text based data structures like XML, JSON you can be sure that the value that is stored in such data structure is teh same that was stored in memory.
When working with floating points this can not be guaranteed since you are changing from floating point to decimal system first. And not every floating point value can be converted into exact decimal system value or vice versa.
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