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In terms of what a logo is, the third is the only one that could be a logo.
The others are just designs that could incorporate a logo. You should be able to photo copy a logo and not lose the meaning and you should be able to create a di - cut.
Simplify then make great designs incorporating said logo.
You should still simplify it to something for business maters should you get (hopefully will) to the point where you need to fax things and have business stationary and what not, but really, the white looks way cleaner than the red.