Topological superconductivity has attracted broad interest because of its connection to Majorana fermions and quantum computation. Kagome materials provide a natural setting in which interesting electronic structures, topological surface states, and superconductivity may occur in nearby energy windows. Here we carry out a systematic first-principles search for binary kagome superconducting candidates with topological electronic states across several structural families AₘBₙ (m:n=3:1; 3:2; 1:1). The screening combines formation-energy and phonon-stability filtering, magnetic-ground-state searches, electron-phonon-coupling calculations, and topological electronic-structure analysis. We identify 286 nonmagnetic dynamically stable candidates for electron-phonon-coupling analysis, among which 84 have estimated transition temperatures above 3 K and seven exceed the ∼ 9 K reference scale of existing ambient-pressure kagome superconductors. In addition, several systems are predicted to host abundant topological surface states near the Fermi level. NbBi is identified as a Z₂ topological metal with clear Dirac-cone topological surface states and a kagome-derived flat band near E_F. Ti₃Si, with the largest estimated Tc=15.2 K in this dataset, shows nodal-line-derived drumhead surface states and selected nodes that survive spin-orbit coupling near E_F. Combining superconductivity with nontrivial topological electronic structures, the binary kagome compounds predicted here represent compact and chemically tunable candidate platforms for topological superconductivity and for exploring kagome-related quantum phenomena.