So ( I'm only saying this because it will help with advice) I'm only 12, almost 13, and I don't know how to go about this. My friend and I want to plan every aspect of this out beforehand so we're prepared, and we don't know whether we should self publish. We might not be taken seriously either way, so what's the best for us?
You can only really answer that for yourself. Do you have a quality product? Are you going to be able to have it edited to professional standards and also get a professional cover for it? If the answer to all three is yes, then I think you're in the right place. It's not impossible that someone your age could be ready. But I think you have to get the work read by people (beta readers, a developmental editor, or whoever) that are going to give you honest feedback and allow you to really assess whether you have something that is ready to go out into the professional marketplace, or whether you've got a lot left to learn before you're ready to put your work out there.
Attempting to publish something - either through a publisher, or by self-publishing - can be a really good experience. Even if you aren't successful or don't sell many copies, you'll still learn a lot by going through the process. I attempted to publish a novel when I was about the same age as you. I didn't manage to find a publisher for it, in the end, but the knowledge I gained by trying is still immensely valuable to me today.
I say go for the self publishing route. But the key, as Steerpike said, is to have it professionally edited. That is more important than anything else. Also, if you can scrape 50 bucks together, you can buy a pre-made cover that will look pretty good, and unless you are a very talented graphic artist, will be much better than you can make. Talk to your English Lit teachers in School. I am sure that they would be willing to help you polish your text. Otherwise, look for writing groups in your area. Best of luck, and keep us informed of your progress.