General guidance seems to be to use a magnification of 30 to 50 times the diameter in inches of your telescope's aperture. An aperture of 80mm is just over 3", so we are looking at magnifications of 90x to 150x.
Your telescope has a focal length of 500mm without the Barlow lens, and 1500mm with the Barlow lens. Since magnification is simply the focal length of the telescope divided by the focal length of the eyepiece, we can see that using the 6mm eyepiece without the Barlow lens will give you a magnification of 83x, and using the 10mm lens with the Barlow will give you a magnification of 150x.
Using a Barlow lens will increase the magnification, but it will also reduce the image quality and also the effective aperture, so the image will not be as bright and contrasty. I would suggest forgetting about the Barlow lens (at least initially), and just work your way up from the 25mm eyepiece to the 6mm. There is no point in using the 25mm eyepiece with the Barlow, since that will only give you 60x magnification, and trying to use the 6mm eyepiece with the Barlow is likely to prove frustrating, if not unworkable.
If you enjoy using your telescope, maybe treat yourself to a 3mm eyepiece, so you can get 167x magnification without the Barlow, but read up on telescope lenses (especially "eye relief"), first. Don't just buy the first lens that you find on eBay.
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