virgi1
You know what's funny? We use the word "design" for software, and you wouldn't think that you could run a contest to pick the design of a software system. But nevertheless you think someone can design his communication strategy & brand identity by a contest, without spending the time to write down the requirements first.
To the OP: my advice is, just don't bother with a contest or a logo. Find someone (a friend) who is good at typography, and ask him to typeset the word "Tarsnap" for you in a way that looks good on that banner. Just use that as a logo, until you have the time & resources to hire someone to do a proper brand identity for you (because that's what you are asking for here, not just a logo)
And this is not an "esoteric question" - you should really have a good grasp on complexity in order to understand the limitations of your system, and when you can use certain algorithms/data structures, and when you can't.
See this write-up: http://www.infoarena.ro/blog/numbers-everyone-should-know - but don't memorize the numbers, that would be pointless - the idea is to get a feel of why complexity is important. (you'll notice for instance that between O(n!) and O(n^2) there is a 2-3 orders of magnitude difference in the acceptable input data size... so your confusion between factorial and n-squared is actually quite big)