There are generally two reasons you will want shrimp: because they look cool or because you need something that can clean your tank. If you need the latter, particularly if you have algae, the best opinion is generally the Amano shrimp, “Caridina multidentata.” Amano shrimp are the go-to cleaner for hair algae and are able to eat considerably more and tougher algae than their smaller ornamental counterparts. Based on my experience, an adult Amano shrimp can clean a whole medium-sized piece of wood covered in Black beard Algae in a few weeks. It is crucial that you maintain high water quality and balanced Co2 and light for the health of the shrimp and to prevent the BBA from growing back. Algae is primarily caused by improper growing conditions, as plants should be able to outcompete algae under the correct conditions. Thus, one must tackle the problem first from its source. Amano shrimp have also been said to damage plant leaves. However, most of the time, the leaf is already undergoing the process of melting/dying, and the shrimp is simply cleaning it up. Another potential downside of Amano shrimp is to breed them you need to change salinity gradually.
Another type of shrimp is the filter shrimp, such as Bamboo Shrimp, which use fans to filter out particles in the water. These shrimp grow considerably larger than any other shrimp on the list and require a decent amount of water flow to filter properly. However, due to their size, they can be placed with fish that would otherwise eat smaller shrimp.
The list of ornamental shrimp is so wide that I will go by water conditions. The most common and popular is Neocaridina davidi (Cherry Shrimp), which has morphs covering basically the whole color palette and beyond. These are generally the hardiest and most adaptive of the ornamental shrimps and are pretty popular in community tanks, although the larvae are likely to be eaten. They can do well in almost any water condition, provided that nitrogenous wastes are low. Cardina Babaulti also has a similar range of conditions but, from my experience, is generally more sensitive.
Next are the bee and tiger shrimps Caridina cantonensis and Caridina mariae, which require a lower pH, GH, KH, and temperatures. The specific parameters depend on the variant you buy and the conditions they were bred in. These shrimp are sister species and closely related enough to hybridize, and often, you will find morphs of these hybrids. On the opposite spectrum is the Sulawesi shrimp Caridina dennerli, which requires temperatures around 80f and high pH, GH, and KH.