If you want to start playing DnD 5e, you don't have to buy anything at all! (Except dice!*)
In fact, there is freely available Basic Rules that you can study to learn more about the game! This covers the most basic stuffs for players and DMs. More books are available to expand your character choices and variant rules. As a DM, Monster Manual is available to further expand the choices of monsters to throw at your opponent.
Character sheet PDF is available to download.
The reason why me and my friends get hooked into DnD so quickly is you can start a session with the bare minimum of character sheets and dice. Of course, you need a DM that has already learned the basic rules!
As a DM, you might want to enhance the play using a map, printed or handdrawn, and token/miniatures for the player characters and monsters, but again, this is not a necessity to start playing DnD.
*You can replace physical dice with a dice roller app, but nothing beat the feeling of rolling real dice.
The Starter Set materials contain exactly what you need to start an adventure with your party!
- You have 5 pregenerated character sheets, meaning you don't have to go through the hassle of creating new characters. Just start the adventure already!
Another blank sheet is available if you want to create your dream character, just make sure you have blank copies!
- 6 perfect dice, just pray to RNGods before you start rolling 'em!
- Lost Mine of Phandelver adventure book, the best book ever, for beginner and veteran players. Easy to run for players and DM alike.
- Basic Rules. Read-me-first, but don't be afraid to make up your ruling if you forget me!
(bring your own pencil, sharpener, and eraser, please!)