The scope of the figures you mention (Tarski, Frege, Peano, Wittgenstein, Russell) makes it a little unclear exactly what you're after. For instance, From Frege to Goedel (as mentioned by Mahmud) is an excellent compilation of early texts in mathematical logic -- you get e.g. Frege, Peano, Hilbert, Zermelo, Skolem, Herbrand, Goedel -- with helpful introductions included, but the focus is on the primary texts, rather than giving a single, unified account of the development of logic. And its relative lack of a philosophical focus means there's nothing like Russell or Wittgenstein to be found. [N.B. Along similar lines to this work, the two volumes of From Kant to Hilbert offer a more wide-ranging (in terms of subject and chronology) cross-section of works in the foundations of mathematics; note, though, that mathematical logic per se is not the focus there.]

Not knowing your background, or your exact goal, I would tentatively recommend Benacerraf and Putnam's Philosophy of Mathematics: Selected Readings. It has a great selection of works by the likes of Frege, Russell, Hilbert, Brouwer, Goedel, Von Neumann, Quine, and so on (and Wittgenstein is mentioned aplenty). In total, you get a lot about the interplay between technical matters in mathematical logic, foundations of math, and also related issues of a more straight-up philosophical nature (if you're into that sort of thing). It too doesn't give a single chronological narrative, but just skipping around the articles in that collection will give you a lot to chew on, and ultimately give you a good sense of the big picture in the development of modern logic.

The scope of the figures you mention (Tarski, Frege, Peano, Wittgenstein, Russell) makes it a little unclear exactly what you're after. For instance, From Frege to Goedel (as mentioned by Mahmud) is an excellent compilation of early texts in mathematical logic -- you get e.g. Frege, Peano, Hilbert, Zermelo, Skolem, Herbrand, Goedel -- with helpful introductions included, but the focus is on the primary texts, rather than giving a single, unified account of the development of logic. And its relative lack of a philosophical focus means there's nothing like Russell or Wittgenstein to be found. [N.B. Along similar lines to this work, the two volumes of From Kant to Hilbert offer a more wide-ranging (in terms of subject and chronology) cross-section of works in the foundations of mathematics; note, though, that mathematical logic per se is not the focus there.]

Not knowing your background, or your exact goal, I would tentatively recommend Benacerraf and Putnam's Philosophy of Mathematics: Selected Readings. It has a great selection of works by the likes of Frege, Russell, Hilbert, Brouwer, Goedel, Von Neumann, Quine, and so on (and Wittgenstein is mentioned aplenty). In total, you get a lot about the interplay between technical matters in mathematical logic, foundations of math, and also related issues of a more straight-up philosophical nature (if you're into that sort of thing). It too doesn't give a single chronological narrative, but just skipping around the articles in that collection will give you a lot to chew on, and ultimately give you a better account of the development of modern logic than will primary sources (IMHO).