I'm completely new to the entire D&D scene, so I thought it would be good to start out by getting the 5e starter set. But, after reading some more information about what's needed to start a campaign (as well as a review of the starter set), I'm starting to think the starter set might not be what I want.
It seems like nearly every website is recommending the 3 core books (Dungeon Master's Guide, Monster Manual, and Player's Handbook), but the Starter Set doesn't seem to contain any of these. Also, it seems that one of the Starter Set's main components is a pre-made adventure, and while that might be great for some, I think that my friends and I would enjoy having a unique adventure in an original world much more. That combined with the fact that the set seems to lack instructions on creating a character and only supports players though levels 1-5, it seems like the Starter Set would be the wrong way to go.
So I assume that I'll have to get my hands on the core books to start DMing, but is it necessary to get the Player's Handbook if I'm just going to be the DM? And since I'm still only in high school, I don't exactly have a huge budget for this, so I was wondering what the best way to get the books would be, budget-wise (sorry if this type of question is taboo, this is my first question).