The classic of alfhors is excellent but terse.
the conway book is boring. It introduces analytic functions as continuously differentiable functions and messes up simple integration . it has messed up a simple problem of integrating multivalued function by avoiding the use of branches.a very wrong text.
lang's is good . emphasis on poewer series is good but formal ower series is unnecessary.
pristley is good but treatment of cauchy's theorem is not satisfactory. it is good at conway but not initial version . churchill is good but gain general treatment of cauchy's theorm is not there.
lanfg and alfhors both use interhange of order of integration. rudin is too te5se and does not mention laurent's theorem! a great lacuna!
my notes partly on wikipedia partly on my website and partly with my students have avoided all drawbacks. we have complete homology vversion of cauchy theorem but do not need homotopy version formaly. also we have original treatment of elementary fnctions