In this article we present a directly diode-pumped high-power Kerr-lens mode-locked Yb:CALGO bulk laser oscillator operating at 1-GHz repetition rate. We report on two laser configurations optimized for either highest average power or shortest pulse duration. In the first configuration optimized for high average power, the oscillator delivers up to 6.9 W of average power, which is the highest average power of any ultrafast laser oscillator operating at gigahertz repetition rate. The 93-fs pulses have a peak power of 64 kW, and the optical-to-optical efficiency amounts to 37%. In the second configuration optimized for short pulse duration, we demonstrate 48-fs pulses at 4.1 W of average power corresponding to a higher peak power of 74 kW with 21% optical-to-optical efficiency. This is the shortest pulse duration and the highest peak power demonstrated by any GHz-class Yb-based laser oscillator. The compact laser setup is directly pumped by a low-cost multimode fiber-coupled laser diode and has a high potential as an economical yet powerful source for various applications.