Are Catholic priests not supposed to get paid or have any belongings? According to some Catholic friends, a Catholic priest is not supposed to own any belongings and they're not supposed to get paid. They are to be "married to the church" in that sense.

Is there an official Catholic doctrine that states this or something like it?
Parish priests do not take a vow of poverty and thus may possess a bank account and have belongings. They also receive a stipend from the parishes they work in. I do not know how much the average stipend is, but I do not think that it is very much. They also receive a Mass stipend for offering the Mass for a particular intention.

Religious priest from a particular Religious Order do make vows of Poverty and may not possess  any belongings. They simply have the use of various things, like a car.