When previewing in the 2D editor, you need to make sure you're viewing the scene at 100% zoom. Otherwise, it's expected that 2D assets will look pixelated or blurry unless they were scaled down (which is not recommended as it wastes memory).
If your artwork has thin borders, you need to make sure it doesn't scaled down too much in Godot. Otherwise, the border will pretty much disappear, which looks bad. This is not exclusive to Godot – it's general art design good practice to ensure your borders are always thick enough.
To avoid issues with rounded edges looking "wobbly", you need to make sure your image's transparent pixels have the same color values as the opaque pixels. For instance, if opaque pixels use the color
#ffffffff (RGBA), transparent pixels should have the color
#ffffff00 (RGBA), not
#00000000 (RGBA). If you use a PNG optimizer, configure it to avoid discarding color values from fully transparent pixels.