On the term Roman Catholic, it is true that protestants first used the term “Roman Catholic Church” soon after the reformation in a vain attempt to suggest that the one true Church was only a part of the catholic (ie universal) church. As you would be well aware it is still primarily used as a descriptor by non catholic Christian sects.
By the same token the term Catholic Church is the most used term by the “one true catholic and apostolic church”, because that is what it is. But some Catholics since as early as the 17th century have always been perfectly happy use the term Roman Catholic Church to emphasise their full loyalty to and faith in the importance of being in full communion with Rome.
It is also true that Roman Catholic Church is often applied to the Western or Latin Church but excluding Eastern Rite Churches which are in full communion with the Holy Father and Rome.
All this is a somewhat complex picture. I am a convert and am just as proud to say to non catholic christians that I am a Roman Catholic as saying I am a Catholic because I am a latin rite Catholic loyal to Rome.
However, more often I use the properly correct term Catholic, because that is what the Church is - the one true church founded by Jesus Christ and which has continued ever thus - as we say every time we say the Apostle’s Creed (eg when saying the rosary) or the Nicene Creed at mass. Indeed when as a boy being raised as a Presbyterian my interest in the Catholic Church was first piqued by the reference in the Apostle’s Creed to the Catholic Church. That started me wondering and with research over time there was but one answer namely - become a real Catholic not a so called member of the (lower case) catholic church which protestant sects claim to be part of, but only by their own authority.
So in summary, Catholic Church is the most correct term to use, but there is also no problem referring to oneself as a member of the Roman Catholic Church, if by that term you mean the latin rite church in full communion with Rome.