The Otocinclus Catfish are the ones that I have heard work best with bettas. I'm pretty sure they need to be in a group of at least three to be happiest, but they're tiny little guys, so it shouldn't be too much a problem. They do great at cleaning up algae too. I got some three days or so ago and they've already got my 10g tank pretty much spotless.
I believe that you would need a filter... but I think you'll need a filter regardless of what type of algae eater or any other fish that you get. I've modified my filter heavily by putting a sponge over the intake and cutting up a plastic bottle to baffle the outflow.