We report a tunable, single-mode vertical cavity surface-emitting laser (VCSEL) format suitable for array operation, power scaling, fiber coupling, and operation in isolated environments such as those required by atom optics. The devices are fiber VCSELs, consisting of a semiconductor gain and mirror structure separated from a mirror-coated optical fiber by an air (or vacuum) gap. The gain structure has polymer microlenses fabricated on its surface, of characteristics suitable to focus the oscillating mode on both cavity mirrors, ensuring stable fundamental mode emission and high fiber coupling efficiency. We demonstrate such devices in continuous-wave operation at 1.03 microm at room temperature, with a single-mode tuning range of 13 nm, laser threshold as low as 2.5 mW, and a maximum fiber-coupled output power of 10 mW.