There is a local tesco not far by the university, food can also be brought in places like pound land, or even order and get asda delivered to the university itself.
i would recommend that you go and visit the money people in student services, who there can set out a budget for any extra costs of living you need.
Money runs out quickly especially if living on campus, as some student loans dont cover the costs of accommodation and leisure.
there are limited jobs around Carmarthen due to locals as well as second and third years getting jobs in the summer.
Before i attended university i wish i had been advised on the overall estimated cost for living and leisure as i feel i struggled a little at the beginning.
I also recommend saving at least 200 for freshers, for lunch's pre-drink and all the activities. (They aren't free)
If you aren't doing a sports degree there is a gym membership fee however not many people know but there is a swimming pool on campus which is free to all students.