Yes,
Character slots allow you to be more versatile to swap to a good char suitable for whatever you are doing.
(Eg. you could have a melee and a long range, and select whichever is best for what you plan to go and fight)
Vaults main purpose is you can keep rare items in readiness for when you need them.
But I would suggest wait until you feel that you need another character slot or vault. Don’t do it just because you think it might make the game more enjoyable, do it because you’re enjoying the game and want to get even more out of it.
Yes, if you do spend money, start with the Beginner Pack and there is no time pressure on it, so you can buy it whenever.