Brady has several decisions to make.
He needs to decide whether he's going to take this further than an appeal to the League with the NFLPA. I say that because I think that the likelihood of an appeal through the League's appeals process, conducted according to the League's rules, is pretty much a certainty.
In order to go make the decision as to whether he should go beyond the League's appeals process, he needs to get legal advice from people who actually know what they're talking about as to what he could do, what it would cost and his likelihood of success. He should probably be talking to someone like Bob Barnett or David Boies. I'm not a lawyer, but the bar for "Defamation" is pretty high when it comes to public figures, so I'm not sure whether that would even be on the table.
If he decides to pursue legal action outside the NFL's appeals process, he needs to decide how far he's willing to go. Money's not the issue as he and Gisele could bankroll a multi-million dollar suit, but he needs to decide if the "Cost-benefit" trade-off is worth it. What would his objective be?
To clear his name? There's really nothing he can do that is going to convince people outside of Patriots Nation of his innocence or lack of complicity in this regard. Minds are made up and they're not going to be unmade. Trying to convince people outside of Patriots Nation that Brady is either innocent or not complicit in "Deflategate" is like trying to convince people that OJ is going to find the "real killer" one day. So, he'd be pursuing that objective for the sake of his legacy, not for any difference it will make in the court of public opinion today. Will that be worth the ten or so million it would cost, with an uncertain outcome in the first place? Only he can make that decision, once he has all the facts.
Scorched earth? Many lawsuits are filed just for that purpose...not to win, but to embarrass the other side in Discovery, etc. Is he angry enough that he would like to tear down the League and those who brought this all to pass? Will that kind of satisfaction be worth the ten or so million it would cost, even if he ends up losing his suit? Only he can make that decision, once he has all the facts.
So, Brady has some big decisions to make that will define not only how many games he plays this season, but his legacy. I don't envy the position in which he finds himself and hope he is getting the very best advice.