Many shrimp will work with certain fish, it all depends on the fish kept and the shrimp species available to you. But shrimp are not strictly bottom dwelling creatures and will roam all over the tank.
I keep cherry shrimp with corydoras catfish, bristle nose catfish, Endlers, guppies, Blue eyes, threadfin rainbows, Khuli loaches, Pakastani loaches and dwarf chain loaches. Another of my tanks has an even smaller species of native Australian shrimp being kept with just spotted blue eyes. While in yet another tank with some more Guppies and peppered corydoras I have more cherry shrimp and the much larger native Typus shrimp. Even when I had black neon tetras they barely made a dint in the shrimp populations, although the Sparkling Gouramis certainly had a good go at it. Some of my Siamese Fighters have also been shrimp safe while others have hunted and eaten the cherry shrimp without mercy.
Depending on the country your in will determine what possible shrimp you could have. Shrimp like Amano, African Basket and glass shrimp are good options. Especially the Basket shrimp if you can provide the right current for them to feed with their amazing net baskets.
I have heard of Micro crabs and I think there is an old thread on this site about them. They might be a good bottom dwelling option for your tank to if they are available to you.
Fish wise as bottom dwellers I love Khuli loaches even if they are very shy and retiring. A predatory option for a larger tank is the spiney eel they are amazing looking fish but again you are unlikely to see them.
Personally I hope to be getting some native fresh water crabs soon and I believe they would be closely related to the Asian Vampire Crabs. Unfortunately I don't really know much about the Vampire crabs, not even if they are fully aquatic but they might also prove to be an interesting tank addition. The only problems might be is that they are escape artists like crayfish and may also snack on fish. But generally I think they stay smaller than crayfish.