OK....my advice....pick something simple. You must first learn to use the weapon as an extension of the hand, and solid weapons are the best to start with....sticks, staffs, etc....nothing flexible...ie: nunchaku, manriki gusari, etc.
I share this sentiment. It's much easier to understand the cause and effect relation your body has to the weapon when the weapon is solid.
With nunchuks, your going to hit yourself. It usually won't be that bad, especially if they're padded. You won't hit yourself in the groin as much as you might think. You hit your elbows and knees a lot. Plus, I've heard excessive nunchuk training can give you serious elbow problems without instruction. Three sectional staff? Whoah... please take your time with that one. A big part of starting with flexible weapons is just getting over the fear of using one. I might recommend padding.
I also wouldn't recommend dual wielding anything for a starting weapon. Not only can it be difficult to learn, but it can also require certain types of strength you haven't developed yet. My escrima sticks weren't too hot until I developed more forearm and deltoid strength, which was particularly weak at the time.
If you have strong shoulders and traps, I would recommend a polearm of some kind.
Now, this is me being a hypocrite. I would also recommend a weapon that has teaching that's relatively accessible to you. It can be difficult to find good information on the usage of a weapon if it isn't taught to you. It can require a lot of research and experimentation with even the best of sources. Take this from a person that's tried it. It can be REALLY hard to understand why certain styles do certain things on your own. Unless your absolutely hellbent on learning a particular weapon, I don't recommend it.
Can it be literally anything? Like shovels? Rakes? Baseball bats? The Monk Spade was the original combat shovel.
Unique....well, it's really more about the application of the weapon itself than it is the weapon. The amount of preferred methods around the world of using the staff is insane. I'm kind of biased to the staff myself.
But if you're really want to use an uncommon weapon, I would posit the cane, hook swords, nagamaki, or any kind of unique polearm. There are a lot. Thing is, good luck learning those.
I would
recommend a more regular weapon if you aren't used to weapons. If you really want it to be unique, try to find an less common style of using the weapon. Or mix a few if that's allowed. The staff (any length) or sword could be good picks for that route.
If you're competing or being judged somehow, don't listen to me so much. I don't know about those things.
Mostly, I would recommend choosing a weapon you enjoy using or has a lot for you to work on. If you get bored of the weapon, that's obviously a problem. Me for example. I think nunchuks are neat, but I got bored of practicing with them after a while.
The wikipedia list of a bunch of weapons!
List of premodern combat weapons - Wikipedia the free encyclopedia
List of medieval weapons - Wikipedia the free encyclopedia