The main purpose of this paper is to present a systematic study of some families of multiple q-zeta functions and basic (or q-) L-series. In particular, by using the q-Volkenborn integration and uniform differentiation on Z(p), we construct p-adic q-zeta functions. These functions interpolate the q-Bernoulli numbers and polynomials. The values of p-adic q-zeta functions at negative integers are given explicitly. We also define new generating functions of q-Bernoulli numbers and polynomials. By using these functions, we prove the analytic continuation of some basic (or q-) L-series. These generating functions also interpolate Barnes' type Changhee q-Bernoulli numbers with attached Dirichlet character. By applying the Mellin transformation, we obtain relations between Barnes' type q-zeta function and new Barnes' type Changhee q-Bernoulli numbers. Furthermore, we construct the Dirichlet type Changhee basic (or q-) L-functions.