I don't know if I will have the time to work on this, but perhaps I can at least ask some questions to help others.
It is an animated Gif, with a funny and discrete animation. If I understood correctly, the resulting logo might be used outside the site, right? So it can be printed on visiting cards, branded letter paper, etc. So that mean no animation, or something as discrete as this one.
Of course, it must be done at a much larger scale, ideally in vector as you point out, to suit all medium.
Can you provide a translation of the writing? (German? Dutch?) Is it a specialized school? Does the vines have a special meaning?
Actually, this logo isn't so bad... I redid the logo of an IT company which had an awful logo. At least, this one is funny. The difficulty will be to keep the idea in a new, simple way...
Good luck in your search! (I will think about it...)

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82% of statistics in signatures are made up. (This is a recursive signature...)
Spreading them is un-original and sheepish. If you agree, copy this in your... wait, no!
No to signature clichés! You are on an art site, be creative!

Yes it is to be used outside this side on paper etc as you mentioned. Like this one is used now just without the rolling eyes on their paper. That is the main perpuse of it indeed. This one is the fun one they have on there website.

The writing means the Ivy (I think the english name is that for the plant) if I would litterly translate it "climing up" than you will understand why it is so suitable. It is a first grade school? for kids from 6 to 12. A local school nothing specialised or so. Yes thanks for mentioning that the vines as explained do indeed have a special meaning.

I agree its not a bad logo for a school but it can be improved I thought especially if it could be intrigated more into there website you feel what I mean? It might not be as easy as when you have a bad logo to start with ... then anything is fine really so I get what you mean in a way it restricts.

I think I answered all your questions if not please do let me know. I hope you feel like giving it a shot and thanks for your interest and for asking good questions!

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Share your kindness, not your hate.
Love the art, not the maker.

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Photography deals exquisitely with appearances, but nothing is what it appears to be. ~Duane Michals

is there a contest section to submit to {i didnt see it} or do we note you with the link?

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Intelligence is like a river ~ the deeper it is the less noise it makes
So stop screaming at me!!!!

Sorry was on holidays either on my journal about it or a note

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Share your kindness, not your hate.
Love the art, not the maker.

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Photography deals exquisitely with appearances, but nothing is what it appears to be. ~Duane Michals

Here is the [link] to the journal btw forgot to mention that

--
Share your kindness, not your hate.
Love the art, not the maker.

---

Photography deals exquisitely with appearances, but nothing is what it appears to be. ~Duane Michals