BP's require very specific temps and humidity, and are often not very tolerant of handling. From what you're saying it sounds like you'd be doing most of the care for this snake, so I'd really not recommend a BP. You are just 13, and from what it sounds like, you have no experience keeping reptiles at all. For someone your age keeping a BP healthy and happy without any parental help could be pretty difficult. Plus, there is a lot of equipment you need for BPs (heat mats, thermostats, heat bulbs or CHEs, ect) that can get kind of pricey (like hundreds of dollars). Research is good, but it's not a substitute for actual experience.
I HEAVILY disagree.

Where does experience start? Ball Pythons are very easy to take care of. Make sure you buy the initial supplies first. The enclosure and thermostat are the biggest expense, and feeding one BP is not expensive -- ask the breeder if the snake is a good eater! Buy the supplies first, obviously, so that you don't have a snake but have to save up for the supplies. I feel like you'd do that anyways, it sounds like you're a thoughtful person. All my racks are used, as are two of my thermostats, except my Herpstat. I seriously have huts and water dishes -- enough for 20 snakes, my turtles, and then some -- plus a snake hook I don't need/want, and some other stuff I got for $40 off of a local reptile forum from someone who was getting rid of his snake selection. I'd look for some things used, like the enclosure and tank decorations. You can build enclosures too, which can be cheap and also further help prove your dedication to your parents, or even provide you with a way to do something WITH your parents to get them involved in your new pet. There are guides online for things like this. The BP can even be free or cheap -- my first BP was a free rescue, which ignited my passion -- I now have 20 of the critters. I had never had a snake when I got my first BP, and expected my first to be a colubrid. I was not perfect at first, I did have a bit of small trial and error with temps and humidity, sure, but fixing it was easy enough. And I got the snake before the research and supplies (would not recommend, but I was saving the animal from a really, really, really bad situation and I had to make a fast choice -- again, very specific situation here, I wasn't looking for a pet snake, I was saving someone else's). I was probably 16 or 17 at the time. Try looking into rescue, reptile show, or breeder instead of an over-priced pet store, who will try to also sell you many things you might not need.

Experience starts somewhere. It starts after you've done good research, which is sounds like you've done. If this reasoning was always used, every person to finally take the leap to gain experience would be deemed irresponsible. Sure, a corn snake might be easier in different ways, but a BP is also easy.

I started raising finicky amphibians and chameleons at 11. The chameleons were admittedly also partially my parents', the toads and frogs were mine. I also acquired a snapping turtle at 13. Those, in my opinion, are harder than a BP in requirements, and probably should not have been a child's pets. I've also had numerous colubrids, and found them to be more flighty, more nippy, more smelly/messy, and, depending on the species, harder than BPs. BPs often use less bedding, many are calm, and there are many resources for them. I was a child who had a passion for animals, read and researched them extensively. If you're 13 years old, and you've written a persuasive essay or two to convince your parents, have read and researched many things, and come to a forum to learn more, I think you're a kid that's ready to have a BP as a pet. I'm not really sure I understand the bias about them not being a beginner's snake. Mangrove snakes, hognose snakes (maybe), vine snakes, sunbeam snakes...obviously hot snakes...large, large constrictors...THOSE are snakes that I'd NOT recommend to you as a beginner/child! While it's true that most reptiles have specific needs, BPs needs' are easy enough to accommodate, and they're hardy enough, readily captive-bred, and more are gentle than not.

If you MUST get a colubrid, I would not recommend a garter -- I love them personally, but they're energetic and often flighty. The few I've had/rescued/worked with (I used to work at a nature center) were not the most fun to handle. Cornsnakes, Ratsnakes, Milksnakes, and Kings are awesome. Keep in mind that some of them get much larger than 3 feet. The Eastern Black Rat is the longest native snake in North America I believe. Most cornsnakes don't reach 5 feet, but I had a male who did.