I agree with nfdc23, notwithstanding here is some kind of 'roadmap' but I am by no means an expert.
I would begin with Brian Conrad's "Several approaches to Non-Archimedean geometry" chapter in a set of lecture notes of a previous AWS http://www.ams.org/mathscinet-getitem?mr=MR2482345 and there are many useful exercises there. Also see the second half of Tate's foreword and Berkovich's foreword to this book for quite an enlightening historical perspective.
This doesn't treat adic geometry at all, but should give a good idea of why one might want a 'rigid analytic geometry' and the many many many subtleties that arise in the theories.
For all the details in say a concrete case like the rigid projective line there is an e.g. first chapter in excellent textbook of Fresnel and van der Put http://www.ams.org/mathscinet-getitem?mr=MR2014891 and the rest of the book has a lot of things that are difficult to find elsewhere. Note this isn't just a translation of the French version, there is a lot more in it than in the 1981 book.
Then I suppose it is a matter of what you are interested in. For me it was things related to Picard--Fuchs, so the book of André was a treasure trove http://www.ams.org/mathscinet-getitem?mr=MR1978691 using the Berkovich dialect.
Then I guess for the adic case which isn't such a massive jump from Berkovich spaces, there are excellent lecture notes of Wedhorn (his webpage) and also its worth noting Huber was an extremely clear writer of articles, and for the perfectoid theory well you are lucky because Scholze is also a remarkably clear writer.