How clearly can I discern the night sky using a small telescope?
I'm sorry, but I am not sure what the question is. If you mean "What can I see of the night sky with a telescope?" then I can give you some idea. First a bit of a warning. For the "starter" telescopes with a 60mm diameter lens, the largest problem is trying to find objects in the first place, even the Moon. Often the tripods and mounts are really shaky. the problem is when you get, for instance, the moon in the eyepiece, then you lock the telescope in place, the moon has disappeared. The small finder telescopes that come on the main telescope are useless. It is best to buy something called a "Rigel Quick Finder" which fastens to the telescope tube with double faced tape, and projects two red rings - a "bullseye," on the night sky and makes it MUCH easier to find objects. So finding objects, and keeping them in the eyepiece can be a really frustrating experience.
If you are in a place with dark skies, without light pollution, you can see nice star clusters. You can see the planets Jupiter and Saturn but they are likely to be quite small. The Moon is wonderful to look at, both with lower power (your 20mm eyepiece) and with higher power (your 10mm eyepiece). It is really interesting to watch the moon every night as it goes from a crescent moon to the full moon, and to see how different it looks as the light changes day by day.
If you live where I do, with pretty bad light pollution, because I am in a suburb of New York City, then the star clusters will seem less impressive. The moon and planets will still be OK. When I want to do some serious observing, I drive for an hour and 45 minutes to a dark sky site about 80 miles from where I live. From that site, I can see the milky way on a clear night.
One of my favorite books for beginning observers is "Discover the Stars" by Richard Berry, formerly the editor of "Astronomy" magazine. The book is a GREAT introduction with star maps, and lists of things to look for with small telescopes, and it only costs about $16.00