I am sure that there will be a great deal of conflict about which of the systems that have been proposed to license will come up. While setting by committee might be a bit odd, system by design (after the foundation is set down) should work better.
I propose a new design with the following design philosophies.
1) A system specific to the setting. This means all the chrome and skill pieces will have names that are tied to the setting, rather than generics. Thus there will be Circus Training rather than Acrobatics.
2) Light to Medium Crunch
2a) The game should be easy to run and playable with just the character sheet infront of you.
2b) One die roll mechanic for everything. (Now that could be 2d6+skill vs 8 or a dice pool with rolls of 4 or better being success, or what ever)
2c) An emphasis of traits granting abilities, than just numbers. So you can have Handgunner, Sharpshooter, Gunslinger (fast draw plus accuracy), Trickshot, rather than Handgun 4.
2d) Traditional Mechanics that any gamer can easily pick up and use, nothing "novel" or odd.
3) Archetypes that give you minimal basic abilities and customization points from there.
If a character has lets say 20 pieces to be complete, the archetype will give you 8-10. D&D has 28 pieces and you only get to choose a few skills (which are not as potent as class abilities) and 4 feats, most are from the class (8-11 out of 28)
3a) Customization should ideally be a point system (1-3 for something), but X number of slots would work.
4) Characters should have a lifepath like arrangement, so people build their history at the same time they build their character.

Good idea, but too early.
I like the idea of a unique system. Fluff and Crunch of a roleplaying game should work hand in hand, and a good setting with good rules can have some serious problems when the rules do not fit to the atmosphere of the game (there were way too many D20 games that had this problem).
Therefore I would suggest to wait with the development of the rules until the winner of the setting competition is announced and then make sure that the rules are fitting to the game fluff. Everything else will just produce another generic system, and there are some pretty good ones already, and some not so good ones.
Let's not reinvent the wheel.
I think that creating a new, unique system would be very interesting -- and overall a nightmare that would be way more trouble than it would be worth.
By using an existing system, we can build upon an existing fan base and network of gamers and products, instead of having to create our own from whole cloth. Using an existing system would be a much better in terms of marketing our game, distributing, and helping it gain popularity.
If the Swarm is really really hankering to generate a brand new system, perhaps that could be a separate project, to be used at a later juncture if/when an opportunity presents itself. But I would suggest not for a first project.
The future
I will also say that I have longer term features planned for the site that would make what Matt suggests a possibility - making a new rules system to go with our new setting.
My thoughts
These are my thoughts, but I am open to be convinced with a compelling argument. :) There are four reasons in my mind for why we should use an existing system.
1) Amount of time to develop
It will take a LOT of time to develop a rules system and playtest it significantly.
2) Draws energy from the setting building
While I imagine not every gaming group is this way, gamers in significant numbers can argue rules forever. If we're arguing rules, we're not working on the setting.
3) Good systems out there
There are a lot of good systems out there that could save us a lot of work while also allowing us to flavor it for our setting.
4) Having a symbiotic relationship
We benefit from the system publisher's brand recognition, and they might even help market our setting directly. The reason they would do that is because it would sell more of their rule books.
Some of these things vary and are debatable with some systems vs. others which is why we'll be having some of those debates under #2 above I'm sure. ;)
Interesting
2) I completely agree with this and find it kind of humorous. I just spent an hour arguing with someone that metamagic feats in DnD 3.5 are more broken than metapsionic feats and therefore should be what we focus on balancing first. I was right by the way XP Anywhos, Mike does make a good point, being what we are by nature as gamers, we at least have the potential to argue about an issue for hours, even if it is just about if something is an issue! Also I find it funny when people argue what is more broken; making spheres that destroy everything or reversing time.
Might I suggest a possible compromise? If I remember correctly (big if) GURPS (it is the one similiar to Chaosium right?) is a rather straightforward and RP driven setting that is also available to us to use. So far, we seem to be placing a lot of emphasis on the RP aspects of the game (where as other games focus on combat like DnD), and as such should find a system that fits what we are looking for. GURPs does that in that characters are not classes but instead individuals with unique skill sets. The system is also rather straightforward and easy to learn and requires only a few dice (percentile for most things and d6s and d8s for damage types). Combat has always been a pain to me when using GURPs (that was my biggest complaint with their Elric of Melnibone series, it was supposed to be combat heavy, but combat was a pain). Might I suggest that we select a system then and make changes to further streamline its various aspects (primarily combat since we'll want a good balance of RP and fighting) and tweek it to fit in the setting we choice?
Personally, I enjoy working on making new systems and tweeking existing ones, so I'm naturally biased towards making our own system. However I understand if we are on a tight-deadline it might be difficult to pull off, but I'll still like to try if it is possible.
Confusion
Sorry, I'm having some problems wrapping my brain around all of this so tell me if I'm getting this right as I try put it in my own words.
1) Skills and abilities will be pertinent to the setting (such as sailing in an ocean setting, and not something like pilot (spaceship) in a fantasy)?
2a) Advanced rules and crazy concepts that made DnD so complex and confusing should be cut out while simplifying the system like 4.0? In short keeping the system as straight forward as possible
2b) Sort of like Nobilis and White Wolf that use only one die type? (so players don't need d20s, d6s, d8s, d10s, etc.)?
2c) So an ability progression might be something like Quick Draw (you draw your weapon as a free action), Quick Reload (you may reload you weapon once a round as a free action), etc instead of Weapon Specialization (+1 to damage with the chosen weapon), Weapon Mastery (+2 to damage with chosen weapon), etc. And while some abilities can grant numerical bonuses, the focus should be on ability granting, not stat boosting?
2d) Straight forward and using established methods for the most part then? (No rolling a d100, dividing the result by your characters strength and compare that against your opponent's dodge score to see if you hit or anything weird like that then?)
3) This part here has me pretty confused. Is this similiar to Call of Cthulu were a character can have a ocupation that grants them a certain number of skill points determined by that occupation and the character also receives a larger number of bonus skill points they can spread over and skill? Also placing a heavier emphasis on skills rather than class level (sort of a quasi classless system and levelless system where skills increase but exp is meaningless, like Chaosium?)
4) So characters would be built following guide lines that would encourage players to come up with a personality for their character as they are stating them out instead of one before the other? If so I'm really for this point as it really helps players connect with their characters and helps new players get into the game easier.
All in all, I am for designing our own system. I've always been divided on what sort of system I'd like to use and I think a lot of it comes down to setting. With the setting Fairy Tale, I can see the system be classless system in which base stats effect a players skills which improve after each session depending how they used them (in other words Chaosium's system). For other settings which are more combat oriented I prefer the generic d20 system (but that can be a nightmare to learn). What I am getting at is I like the complexity and customization of D20 in combat parameters as it actually is mostly straight forward in combat where as I like the RP benefit and character versatility / depth that comes from a class less / level less system that focuses on skills. I think designing our own system would be a good idea. If I understood you right, I agree with your points for what we should focus on when designing the system but would like to add that if we do this that we should also make sure we keep combat streamlined as well.