Conventional compact spectrometers have a fixed spectral resolution and cannot resolve the polarization properties of light without additional optical elements, while their larger counterparts are bulky and costly. Here, we demonstrate multiple off-axis meta-lenses in the visible integrated on a single planar substrate. They possess both focusing and strongly dispersive properties and are designed to provide different spectral resolutions as well as working wavelength ranges on the same chip. We realize a compact spectrometer using only these meta-lenses and a CMOS camera and achieve detector-limited spectral resolutions as small as 0.3 nm and a total working wavelength range exceeding 170 nm for a beam propagation length of only a few cm. In addition, this spectrometer has the capability to resolve different helicities of light in a single measurement. This chip-camera setup represents the most compact configuration so far achieved for a spectrometer with similar performance and functionality, and its compatibility with large-scale fabrication processes makes it broadly applicable.