Which of the UTP cable categories is recommended as 100Base T media? CAT2,CAT3,CAT4,CAT5

If you have a 10GBase-T stream attempting to transport over a 100Base-T link, you're going to totally max out the 100Base-T. Only expect to get 100 Mbit/s end-to-end.

Any transport system is only going to be as fast as its slowest link.

OTOH, sending 100Base-T traffic over a 10GBase-T link will work just fine - you'll get the full 100 Mbit/s all the way.

Speed

300 feet

RJ-45 or 8P8C modular connectors