Interested in logotype, - don't need a cartoon character. However if a glyph of some kind is incorporated in the logotype (I believe that is called a logomark) we would be delighted to use that as our website favicon, app icon, on t-shirts, etc. The Sputnik logo is built that way - we use the full logotype + logomark for the website but use the three curved "radio" lines logomark as app icon and to brand various products.
Primary use is on website and app, also business cards, letterhead, t-shirts, vehicles (someday! dreaming here).
What industry do you think your business is most related to?
What colors do you want to see in your design?
To give us an idea of the overall feeling of your brand, let us know which styles you lean towards