What you need to do is sit down with a priest and explain everything to him and he can help both of you sort out what needs to be done. Circumstances will dictate the proper advice and we don't have all that information here.
One thing is certain, you don't have to first become Catholic or, for that matter, ever become Catholic; Catholics can marry non-Catholics, provided they themselves are free to marry and the spouse-to-be agrees to raise the children Catholic.
That being said, becoming Catholic is a wonderful thing for your family, so both parents are on the same page, but it is also good for you. We hold that the Catholic Church is the Church founded by Christ and the historical evidence bears that out.
That's true despite all the scandal, warts, and evil you see today. In a weird way, its current state almost confirms its authenticity — for there has been betrayal, deception and scandal since Jesus found His Church — just look at the Twelve Apostles. We all need Jesus and the grace He gives us through the Sacraments, and the many treasures of the Church for, in the end, it is all about getting off this planet alive!
I am thankful that I am a Catholic because I need every tool the faith has given me to help me become more like Jesus — I would be a pitiful failure without it . . . .and I am still a long way from success — it's a lifelong journey!
Finding a good priest and parish is your first step, so I would consult good practicing Catholics in your area that may be able to offer a recommendation.
Sadly, not all priests are equally good.