We present our studies on a compact high-performance continuous wave (CW) double-resonance (DR) rubidium frequency standard in view of future portable applications. Our clock exhibits a short-term stability of 1.4 x 10(-13) tau(-1/2), consistent with the short-term noise budget for an optimized DR signal. The metrological studies on the medium- to long-term stability of our Rb standard with measured stabilities are presented. The dependence of microwave power shift on light intensity, and the possibility to suppress the microwave power shift is demonstrated. The instabilities arising from the vapor cell geometric effect are evaluated, and are found to act on two different time scales (fast and slow stem effects). The resulting medium-to long-term stability limit is around 5.5 x 10(-14). Further required improvements, particularly focusing on medium-to long-term clock performance, are discussed.