To use the same account (and characters) on either platform, you need both a PS4 licence and a PC licence registered to the same account.

But to play with your brother, you'd each need separate accounts, since the same account cannot be logged into multiple characters simultaneously.

So you might need anywhere between 2 and 4 copies of the game, depending on what you want to do. If one of you will always play on the PS4 and the other will always play on PC, then one copy of each type and each of those registered to different accounts will work. But if you want to alternate between sometimes playing on PC and other times on PS4, and your brother does too, then you need a PS4 copy for yourself, a PC copy for yourself, a PS4 copy for your brother, and a PC copy for your brother, with both of your codes registered to one account and both of your brother's codes registered to another one.

And once you get to Heavensward or Stormblood, you'll need just as many copies of that.