Not every space object is created equal, and as matter of fact, space used to be quite a tailor-made endeavour. You can look for several different types of satellites and below you can read about some of them.
Earth observation satellites carry various sensors designed to provide multispectral views of the Earth. They usually fly in Sun-synchronous orbits and are, therefore, visible from anywhere on Earth.
These satellites observe and help predict the Earth's weather. Two groups of satellites are in this category, those in low-earth orbits and those in geosynchronous orbits. To view satellites, mainly those in low-earth orbits, are viewable. Satellites in geosynchronous orbits are too far away to be observed without a relatively large (and expensive) telescope.
This class of satellites relays communications signals between different points on the Earth. Communications satellites use three types of orbits: low-earth, Molnyia, and geosynchronous. For the purposes of satellite observation, only those in low-earth orbit are of interest.
Navigation satellites send out radio signals that are picked up by special receivers and used to precisely locate the receiver's position anywhere on or above the surface of the Earth. These satellites typically orbit in constellations consisting of 10 or more satellites. There are 4 main constellations: the US GPS series, the Russian Glonass, The European Union Galileo and China's BeiDou series. The satellites in these constellations are in orbits that are too high to be seen without a telescope. Several spent boosters from their launches are still in orbit and make good viewing targets.
There are several missions of interest to the military, like reconnaissance (spy satellites), communications, early warning of missile launches and weather predictions. Many of the best satellites for viewing are the spy satellites in low-earth orbit. Because of the nature of their missions, the satellites tend to be large and in very low orbits. Unfortunately, the data for this class of satellites is not published by any official agency. Occasionally, you can find data from amateur groups who compile these sets from their observations.
Before the advent of mega-constellations, most of the objects in orbit were falling into the category of "debris". This includes spent rocket bodies that accompanied a payload into orbit, payloads that are no longer active, pieces of space junk resulting from the explosion of a satellite in orbit and such exotic items as wrenches, cameras and gloves accidentally dropped by astronauts and cosmonauts. For satellite viewing, the best objects in this group are the spent payloads, as many of these objects are relatively large, the size of a passenger bus or more, and are pretty easy to see.