We generate a tabletop pulsed relativistic electron beam at 100 Hz repetition rate from vacuum laser acceleration by tightly focusing a radially polarized beam into a low-density gas. We demonstrate that strong longitudinal electric fields at the focus can accelerate electrons up to 1.43 MeV by using only 98 GW of peak laser power. The electron energy is measured as a function of laser intensity and gas species, revealing a strong dependence on the atomic ionization dynamics. These experimental results are supported by numerical simulations of particle dynamics in a tightly focused configuration that take ionization into consideration. For the range of intensities considered, it is demonstrated that atoms with higher atomic numbers like krypton can favorably inject electrons at the peak of the laser field, resulting in higher energies and an efficient acceleration mechanism that reaches a significant fraction (≈14%) of the theoretical energy gain limit.