Notes on the numbers
Magnitude measures brightness backwards: the smaller the number, the brighter. From a dark country sky the eye reaches about magnitude 6 for stars; 10×50 binoculars about 9–10; a 6–8-inch telescope about 13–14. Galaxies and nebulae spread their light out, so they look fainter than a star of the same magnitude — the size and surface brightness on each object page say how much.
The counts on the tabs differ a little from the original totals of 7,840 and 5,386: OpenNGC lists some entries as separate components and leaves out duplicates and objects that turned out not to exist.
Up tonight means the object climbs higher than 20° above the horizon at some point while the sky is dark at your place. Low objects shine through more air and look dimmer. The list ignores trees and buildings; to account for them, set up My view and check the object page.
Data: OpenNGC by Mattia Verga (CC BY-SA 4.0), d3-celestial by Olaf Frohn (BSD 3-Clause), HYG star database by David Nash (CC BY-SA 4.0). Photos come from Wikimedia Commons and the DSS2 sky survey via CDS; their credits are on each object page.