The kind of bike you need is what is appropriate for how you ride. If you live in a flat area and ride with your family, a hybrid is just fine. There is no need to compare yourself to racers.
I'm 57 and I have step grandchildren. I bought a comfort hybrid about 9 months ago and thought it was the greatest bike. But since I did not like riding alone, I joined a beginners class with the local bike club. That class really improved my mileage and my learning of safe biking rules. Since I live in a hilly area, after 3 months I realized that the bike was not good enough for what I wanted to do. I bought a flat-bar road bike/hybrid that was lighter weight. It still was as easy to ride as the other bike, but I could keep up with the others better. It's still not a 'real' road bike, but it's what I need now.
Most of the ladies in the club are in their mid 60's and can ride circles around me. So, improving to that level is not impossible. I went from the 10 miles rides to usually 20 miles, but my longest is 40.
So, you can do that too, if you want to. The age is not the problem. I don't intend to do centuries or race either. I'd like to be able to keep up with the 60 year olds. Have fun on your bike. If you feel like you need to upgrade later, you can do that.