I would suggest to start with "The Search for Mathematical Roots, 1870-1940" by I. Grattan-Guiness, which has some chapters on Cantor, which you can skip if it really doesn't interest you, so that you begin with chapter 4, which is on Pierce and Frege.  It has less on Tarski than you might want, in which case you can read the Feferman biography called "Alfred Tarski: Life and Logic".  It may also have less on Wittgenstein than you want, but there are myriad supplemental materials there.