I've never attempted it before but some species of peppermint shrimp are supposed to be very easy. I believe they mate just fine without encouragement of any kind but expect the babies to get predated on if you don't move them into their own tank. If you do move them they're easy to raise because you only need a basic tank setup and baby brine shrimp to feed them on.
Some species of larval shrimp require special tank conditions - something to do with circular motion of the water I believe? Someone else may be able to provide more info on this.
But I think in all likelihood peppermint shrimp would be the easiest to start out with.