We present significant advances in laser wakefield acceleration (LWFA) operating at a 1 kHz repetition rate, employing a sub-TW, few-femtosecond laser and a continuously flowing hydrogen gas target. We conducted a comprehensive study assessing how the nature of the gas within the target influences accelerator performance. This work confirms and elucidates the superior performance of hydrogen in LWFA driven by few-cycle, low-energy laser pulses. Our system generates quasimonoenergetic electron bunches with energies up to 10 MeV, bunch charges of 2 pC, and angular divergences of 15 mrad. Notably, our scheme relying on differential pumping enables continuous operation at kHz repetition rates, contrasting with previous systems that operated in burst mode to achieve similar beam properties. Particle-in-cell simulations explain hydrogen's superior performances: the ionization effects in nitrogen and helium distort the laser pulse, negatively impacting the accelerator performance. These effects are strongly mitigated in hydrogen plasma, thereby enhancing beam quality. This analysis represents a significant step forward in optimizing and understanding kHz LWFA. It underscores the critical role of hydrogen and the imperative need to develop hydrogen-compatible target systems capable of managing high repetition rates, as exemplified by our differential pumping system. These advances lay the groundwork for further developments in high-repetition-rate laser plasma accelerator technology. Published by the American Physical Society 2024