Well, if you've got a background in philosophy, then you'll hit the ground running. I'm a fucking movie nerd who's never taken a single philosophy class. I just read this shit so I can tell other movie nerds who use it that they're stupid and wrong and the people they're quoting are also stupid and wrong. In order to do that, though, I have to make sure I know what I'm talking about, so I'm stuck doing a hell of a lot of reading
The easiest way to proceed will probably be to settle on the Derrida shit you want to read first.
Of Grammatology is Derrida's main calling card, and that's the one where he goes through Ferdinand de Saussure and his
Course in General Linguistics and Jean-Jacques Rousseau and his
Essay on the Origin of Languages. However, I'd probably recommend the edited collection
Writing and Difference, where you can go one at a time through easier-to-manage essays rather than giant volumes of crap and take the thinkers and texts he selects one at a time. So there'll be one essay where he's dealing with Michel Foucault, and you can go one-to-one. Then something with Husserl, then something with Freud, then something with Hegel, and on and on down the line.
I also have to recommend his "fight" with John Searle. In 1972, Derrida wrote an essay called "Signature Event Context" in which he critiqued J.L. Austin's
How to Do Things with Words in which Austin developed his theory of "performative utterances." Searle wrote a reply to Derrida in which he basically called him out on (a) not making sense and (b) failing to understand Austin. Derrida then replied in one of the most hysterical replies you're likely to find in philosophy. The mask was gone and it was the flailing hysterics of someone whose safe space had been invaded. In a way, it's actually sad to read, but it's proof of what Peterson always mentions about how these types of people don't believe in and have no desire to enter into a dialogue with you. They just want you to accept the nonsense on faith, fall in line, and help push the bullshit forward.
Best of luck. I hope you come out the other side still believing in philosophy