(How) can I store and cook leftover rice so it isn't soggy?
It seems that the secret to re-heating rice is to use a little bit of liquid during the re-heating process.  StillTasty suggests adding 2 tbsp. of liquid per cup of cooked rice, and about 1 minute on high for each cup in a microwave (5 minutes flat for stovetop re-heating).  

Another thing it hints at, though doesn't outright state, is that cooked rice should be stored in an airtight container separate from the food it is meant to go with - this is likely where I went wrong, and why my rice is always soggy and unpalatable. 

It also suggests that 2 hours is the maximum allowable time for cooked rice to be kept at room temperature, and that it can stay stored in the refrigerator between 4-6 days, or up to 6 months if frozen under ideal conditions.