the first interrupt you need to use is the UART. (that is if you use it).
Polled UART processing is, at best, slowing down processing and, at worst defective.

Make a "ring buffer" with a length of some power of 2 (it makes things easier, you'll see later) I would suggest 8 or 16.

then 2 pointers, I call them "store" and "fetch"

After proper initialization you will know that when fetch and store are identical, there are no characters received that have not been processed,

For refernce search on ring buffer

Erik