Advice on private sales in Utah?

I'm not sure if this is the right sub for this, but hopefully you guys can help out. I'm looking to buy my first gun, and I really want a cowboy style revolver (yes I know it's not a practical gun but they're cool and I want one). The only issue is that to buy one from a dealer you have to be 21, which I am not. HOWEVER I could buy one from a private sale and it would be completely legal. So what I'm wondering is 1. is that even a good idea? Some things are legal but are still a bad idea, like smoking. 2. Would I need a background check for a private sale?

Any help or advice is greatly appreciated, and hopefully this is enough detail.