If you are drawn to the Roman Catholic Church, then go find your local parish, ask to speak with the priest, and ask about RCIA (Rite of Christian Initiation for Adults). RCIA is the course for those interested in converting to the Catholic Church--I myself went through it five years ago. Don't worry--it's free, and you'll have a sponsor to answer any questions you have, pray for you, be a sounding board for you, and just be there to support you in your journey of discernment.
Orthodoxy is an option that you should indeed be aware of, and explore both Catholicism and Orthodoxy if you feel so inclined. Both of those churches have been around for 2,000 years, and neither are going anywhere anytime soon. Plus, it never hurts to be informed
However, should you feel inclined towards the traditions of Orthodoxy, towards the liturgical, spiritual and theological traditions of the East, know that there are also
Eastern Catholics out there--we are autonomous churches that have all the same traditions, Saints, liturgical rites, theology and spirituality of the Eastern or Oriental Orthodox, while being in full communion with the Pope of Rome, and holding to all the doctrines of the Catholic Church. The Roman Catholic Church is only one independent Catholic Church out of 23 in total--the other 22 are all Eastern Catholic, and as a Catholic, you would have full and complete access to all of them!
I as a Byzantine Catholic attend Mass, receive Confession and receive the Eucharist at a Roman Catholic Church while I'm at university due to convenience, but at home, I attend Divine Liturgy, receive Confession and receive the Eucharist at my home Byzantine Catholic parish, and this is completely normal, and even commonplace.