Is there a common metric to measure telescope power? It is rather hard for me to compare telescopes due to the various numbers used.
600mm focal length and a 50mm diameter and eyepiece is a 12mm.
VS.
Focal length of 500 mm and the objective diameter is about 90 mm, Using a 3x Barlow Lens.
Is there something like an APR for telescopes?  Is there any objective rating system?  Most of the review videos just sound like sales pitches.
GC_
Is there a common metric to measure telescope power?... Is there something like an APR for telescopes?... Is there any objective rating system?

If there was one single metric, it would be aperture, but there really isn't because there are several other aspects that can make one telescope much better suited for viewing than the other.

The diameter is most of the power of a telescope, dim stars always appear brighter, doubling the diameter of the objective results in 4x the area to collect light, so the apparent magnitude of a point object like a star goes up by 1.5 or so.  Also a greater diameter increases the detail visible to the point where you can use more magnification, or at least make the same view much sharper.
The ratio of the focal length to the diameter is the &quot;focal ratio&quot;, for instance a short focus reflector with an 8&quot; mirror and a 32&quot; focal length has an f4 ratio, and a refractor with a 3&quot; lens and a 36&quot; focal length has a f12 ratio.
Shorter focal ratios are generally better for observing extended objects such as galaxies and nebulae since the available light is concentrated into a smaller angular size for the image, whereas long focal ratios are better for observing detail such as planetary observations and splitting close double stars because a given eyepiece will result in greater magnification. I take it you're a novice at observing astronomical objects, so I'd recommend dipping your toe in the water by buying a relatively small middle range focal length scope for general observing without breaking the bank.  Oh, and avoid those department store telescopes which are shaky and don't have good optics. Claims of 700x magnification don't do anything but make the wind blown blur more apparent.