Looking at most astronomical object through a Telescope is boring because you only see a white ball or point every time. Such targets would likely only be interesting with spectroscopy analysis.
There are however some objects that you can see the structure of even with an amateur telescope, and that makes them very exciting.
Some good ones:
- The Moon, notably crater detail.
- Saturn. Clearly visible to the naked eye, but looks like a ball. But under an amateur telescope, you can clearly see that there is a disk. Clearly discerning that the disk is a ring, i.e. seeing the gap, is a bit harder though.
- Jupiter. Clearly visible to the naked eye, it is quite huge. The four Galilean moons, being Earth-sized, are incredibly clearly visible, tested on Celestron NexStar 4SE 25mm/9mm eyepiece. Colored gas clouds are hard though, you will likely just see it bright white. www.reddit.com/r/telescopes/comments/35xrbb/how_can_i_see_the_color_of_jupiter_with_my/
- a double star. As mentioned at www.relativelyinteresting.com/10-astronomical-targets-new-telescope/ Albireo are incredibly separated. Also it is is easy to find manually being in a major well known constellation. It is no wonder it is not quite even known if they are gravitationally bound or not!
- Andromeda Galaxy. This is when things start getting hard. You can see a faint cloud, but it is not super clear that it has a center.One important understanding is that it is not possible to see stars outside of the Milky Way by naked eye.It is at this point that you start to learn that pictures of faint objects require longer term exposure and averaging of the images taken. For this you need:Just looking through the scope to immediately see something is not enough.
- a digital camera attached to the scope
- a computerized scope that slowly moves to track the point of interest
- image processing software that does the averaging
Video "Andromeda Galaxy with only a Camera, Lens, & Tripod by Nebula Photos (2020)" gives a good notion of expectation adjustment.
With Telescopes however, it is possible. www.quora.com/Can-we-distinguish-individual-stars-in-other-galaxies-or-would-it-be-equivalent-to-say-we-know-there-are-other-forests-of-stars-galaxies-but-we-cant-tell-the-individual-trees-stars-What-is-the-farthest-individual/answer/Jerzy-Micha%C5%82-Pawlak contains an amazing answer that mentions two special cases of the furthest ones:
- gravitational lensing observation
- a star that is far but visible because its light is reflected by a nearby nebulae
But what we can definitely see are globular clusters of galaxies. E.g. the article en.wikipedia.org/wiki/Messier_87 basically gauges the size of galaxies by the number of globular clusters that they contain.