I have played piano since the age of 5. I started by taking lessons from the nice church-lady down the street. My best friend was taking lessons so I begged my mother. Probably ten minutes after I started lessons, my friend quit! My mother wasn't so accommodating, so my lessons continued. Everything that I played was classical.
When I was in high school, I began taking lessons from an eccentric classical pianist... He was quite odd and there were rumors that he was running some sort of cult out of his home. It was a mansion on a hill and there was always an abundance of slightly stoned looking young men in residence. As a result, my lessons with him didn't last long because I was uncomfortable and my parents knew it. I never took another lesson after that.
In retrospect, I don't think that I ever really enjoyed playing. I was forced to play and to practice. I also played clarinet, bass clarinet, saxophone and some percussion in school bands. I enjoyed those a lot more...There was something to be said for being a part of something larger than myself (the band). To this day, I still miss participating in a band, but I don't miss the piano.
Over the years, I have used our out-of-tune piano or (more often) our keyboard to help my children to understand their music parts. In recent years they have gotten to the point where they don't really need me in that capacity anymore.
One is a music major in college and the other will be one next year.
As to whether or not you would like playing the piano, I would have to say to go for it. As a kid, I got into playing for the wrong reasons and developed a resentment. In your case this is something that you want to do...for you! At your age, I have to assume that you know what you want and that you will practice regularly to pursue this.
As to whether or not you should purchase a used piano, I would suggest that you consider some other factors... Are there other people who would be disturbed by your practicing? If so, then a keyboard might be a better choice for you, especially if it is equipped with headphones and a foot pedal. Would a piano have to be moved often in your house? If so, a keyboard would be better. The simple act of moving a piano can dramatically affect the tuning, costing you more money, more frequently. As someone else alluded to...The climate in your house can affect a piano. I can remember my mother placing pans of hot water under the piano because of the dry air in our house during the winter. Keyboards are not affected by climate.
If you really want to play the piano, you will. Just understand that it takes some time to get really good. Be realistic in your goals and don't be too hard on yourself if you miss a note. Play for yourself to make you feel good. Don't do it for anyone else!