What's appealing about #4 is the "3d circle"---that style of an element that has depth, although in this case without the vine or with a very subtle version of it. Referring back to the logo ideas (
http://openvine.com/logo-ideas.html), I would be interested in seeing the top one on that page but with the style of button in #4 or #18 (but without the black vine).
What I like about #24 and #26 is the simplicity of overall design, and the next step would be to make the individual non-text elements with a "3d" look.