We describe the fabrication and characterization of a new surface-electrode Paul ion trap designed for experiments in scalable quantum information processing with Ca+. A notable feature is a symmetric electrode pattern which allows rotation of the normal modes of ion motion, yielding efficient Doppler cooling with a single beam parallel to the planar surface. We propose and implement a technique for micromotion compensation in all directions using an infrared repumper laser beam directed into the trap plane. Finally, we employ an alternate repumping scheme that increases ion fluorescence and simplifies heating rate measurements obtained by time-resolved ion fluorescence during Doppler cooling.