Here is a sampling of a couple concepts for logos that were created for a couple websites.
The first four images represent a logo created to brand this site. I went through a couple concepts. The first version, I tried to take advantage of the letter R in both words and create from there. Later, the design changed. I tried to be a bit more visual in a minimal way. I went through various color combinations. Finally, I decided on the blue/green combination.
The other logo was created for a T-shirt design website. I went for a vintage badge look. The first version, the color combination seemed a bit cold. Changed the harsh olive color to a kinder-gentler blue. And changed the tint of purple to a regal shade of purple.