When I was 15, a friend of mine was going to a Backstreet Boys concert. Her parents did not like the idea of her going alone, so they called my parents and asked if I could come along (amusingly enough I did not know about this before my parents had already said yes). That's the only larger concert I've been to. Other than that, I've mostly just gone along with friends to smaller concerts that they wanted to go to. The only concert I've attended in my adult life for my own sake was Lindsey Stirling, which was really cool - especially since she ended up doing her Zelda medley towards the end of the show.
I'm actually not all that big on concerts, to be honest. I find them noisy with all the shouting from the other people attending. Also, I'm just not a huge music fan. I tend to think of music as a means to add atmosphere to something else (like a movie, game, video, etc). There are very few artists bands that I would be interested in seeing a live performance for, but Nightwish, Within Temptation and Sarah McLachland would probably be cool.
I haven't personally met any singers, nor do I care to, really (as previously mentioned, I'm just not a big music fan). But I do attend a lot of conventions, and meet actors from various television shows that I love (which is more my medium). That is something I really enjoy. My advice when meeting someone you're a fan of face to face, is to do everything you can to stay calm. It's really hard to do the first couple of times, but if you can pull it off, I can pretty much guarantee you you'll have a better experience. Celebrities tend to feel more relaxed if the people they meet stay calm, and they are more inclined to have a proper conversation with you appear calm and collected.
To give an example, I've met Eliza Dushku (who played my favourite character in Buffy the Vampire Slayer) twice in my life. The first time I was so starstruck I couldn't get a word out, so our encounter was short (albeit nice and memorable), because she was the first actress I had met. Eight years later, I met her again - this time I already had plenty of experience meeting actors, and I ended up having more of a proper conversation with her, including a fistbump at the end, lol.
So, do whatever you can to stay calm during the meet'n greet, and you'll more likely end up with a truly memorable encounter