Ghost shrimp survival rates are entirely dependant on betta personality. From what I've read and experienced, the odds aren't great. They're cheap though, and a great test to see if you should make the investment in cherry shrimp, who are pretty similar in size, shape and longevity. As for reproduction, don't expect them to reproduce if there are other tank mates... The babies will get eaten almost immediately.
Amanos on the other hand... Are my all-time favorite tank mate. They get to be about 2 inches or so max and I've had absolutely no problems getting them to peacefully live with my bettas, presumably because of their size. They're not an ornamental shrimp, which means they live almost 3 times as long as the cherries and do an unreal job with algae and bottom feeding. If you have live plants of any sort, I'd say you're silly not to have these guys. Even without plants, I'd say they're a good investment. Personally, I would never have a tank without amanos. Not only do they look cool, but they have the highest cleaning capacity of any tank inhabitant I've ever kept.
Plus, they sometimes hitch rides on betta tails, which is absolutely hilarious. Oh, and they won't reproduce, since their larval form requires salt water until they're in a juvenile state. Weird, but true.