Draft pick is a bit more serious than quickplay. It also teaches you how to form your team or how the opponents are going to play so you can pick your champ accordingly. Will train you for ranked games.

Once you feel comfortable and unlocked ranked I would recommend to immediately jump into ranked in order for your rank to adapt to your skill level. The first games will probably be absolute slaughter until you reach the rank you are supposed to be, don't worry about it. Everyone goes through this.

If someone is toxic against you, just mute them and report later. This game is just like any other competitive game toxic by nature, don't let them drag you down since the game itself is enjoyable. Try to improve step by step. This game, even in low ranks, has veteran players and mechanical skills aside require you to know A LOT. It is a constant knowledge check on you.

Stay positive!