If the extra $100 for 64 GB is doable, I would go for that option, particularly if you are planning on keeping the phone for a while. As you likely know with your 5c, a 16 GB phone only has about 12-13 GBs of usable storage as the operating system takes space. The 64 will allow you so many other options from music, photos, books to movies, etc. You will use it....
Regarding plans, they seem to change from month to month, a new deal here and then one there. I have AT&T and I looked about 3 months ago - there was a small discount involved but not enough to sway me one way or another as the monthly charge over two years is so much larger than any small savings. I would call one carrier and then another and ask what is the best they can do for you.