Nice first try! Generally when engaging in astro-photography, there are 4 main things to take into consideration:

1. Shutter speed - This indicates the speed at which the shutter of the camera closes. The slower it is, the more light it captures, which is ideal in this case. A good rule to go by is the so-called "Rule of 500", in which you can see how long to expose before star trails start to appear. You basically take the number 500 and divide by the focal length of your lens. So for example, if you set your lens at 18-mm, then 500 / 18 ≃ 27 seconds.
2. Aperture - Set the aperture to the lowest possible f-stop value. Since our goal is to capture light at night, the camera lens should be as wide-open as possible.
3. ISO - ISO should ideally (for me personally) be between 800-1600. The more you increase ISO, the more likely you'll see noise (In the second image you provided it is actually visible, from the purple/pink dots all around the sky.)
4. Focus - Keep it manual. When setting it to manual, point to a singular star and try to adjust the lens till that star appears as small and sharp as possible.

As far as editing goes, less is more. Basic stuff to experiment with and toggle:

• Exposure (Increase)
• Contrast (Increase)
• Shadows (Increase)
• Whites (Increase)
• Highlights (Decrease)
• Blacks (Decrease)

At the end of the day though, editing is up to you and also depends on the raw file itself.

Good luck!