Congrats on your first con! Are you just doing a day or a weekend?
1. Remember to eat, I know it feels like the excitement can fuel your body, but trust me you'll regret going the whole con without eating. Some of us actually stop for lunch, others just bring some healthy/energy filled snacks (and no I don't mean energy drinks).
2. Make sure you have everything you need the night before you leave, nobody wants to be late because they're rushing around the morning of trying to grab everything or even end up forgetting something in the rush. This means cosplay pieces, snacks, even fill up on gas the night before, oh and your money so you can buy awesome stuff.
3. Bring deodorant, even if only doing the con for a day. You're going to be stuck in a room with thousands of people, you'd be surprised how much AC that eats up. You will sweat, especially if it's in the summer or if you're just from a warmer place in general.
4. Bring a good attitude! Most people are excited and in a very happy mood anyway at a con, but there are some jerks. Starting off with a good attitude could help from becoming another jerk if you have the misfortune to run into one, or seeing your good attitude might pull somebody else out a funk if they just ran into one of the people with a negative attitude or even if for whatever they're in a blah mood to begin with.
5. Have fun!
If you're staying multiple days then it really boils down to pre-planning. Making sure you've made hotel reservations prior in advance, again that everything is packed, even planning where you'll be eating or if your hotel room has a little kitchenette in it, it also means having somebody that will be checking in on or house or looking after your pets while you're away.
As for telling your parents you are cosplaying.....
Be polite and respectful when telling them, don't act like a brat.
Explain to them that this is what people do to show appreciation for a fandom they like, does everybody cosplay? No, but it is so much fun!
It also lets you meet other people that are into the specific fandoms that you are, a lot of people meet at cons and become friends, either just somebody to talk to online or even ones they actually hang out with and it's because they saw the other person cosplaying a character from a series they like. Does this mean you're going to get along with every person cosplaying from your favorite series? No, however at the least it gives you both a few minutes of heightened enjoyment from conversation and cosplaying at the con. (Note: I'm assuming you're about high school age, so you might want to phrase it that it could lead you to making friends of your own age, I know some parents -and rightly so- getting a little nervous about their kids meeting new people)
I've used this too when trying to explain cosplaying to a cousin,
"You know how you're little sister reaaaaally likes the Disney princesses and couldn't decide which one she wanted to be for Halloween and you're mom had to buy like five different outfits? Well, cons are for older fans who still have things like that they love and not only can we celebrate our fandoms on Halloween, but now there are these big conventions for every fandom imaginable and you get to dress up for multiple days most of the time and meet people you actually have interests in common with." I'm the only dork in my family that's really into this kind of stuff -though I think I'm turning my mom into one- lol, It's not the best explanation, but he seemed to understand that we do this for enjoyment, to show off skills we learned while making our cosplays, and to meet people with similar interests, and of course showing off our love of our fandoms.
Speaking of skills, if you're making your cosplay, you could tell them that it'll help you learn how to sew and such.
Try talking to them separately, pick the one you think is more likely to say yes after explaining your case, then have them go with you to talk to the other one as back up.
As for them thinking your show is weird, I've been watching anime since i was ten or eleven, and I've seen some that I think our weird too lol, that's all a matter of personal tastes. The point is to explain to them that that's one of your animes that you love and you really want to do this all while, like I said, being respectful, they are your parents and their decision, like it or not, is the one you have to go with. You'll get a lot further and probably the answer you want if you take the time to explain to them why instead of demanding or acting like a temper tantrum throwing toddler.
I hope they say yes and you have a lot of fun at your first convention!