One of the nice aspects of Git is that it doesn't mandate the use of a particular client. There are several to choose from, and they are all compatible with each other. Most of the clients use one of several core Git implementations, which is good for stability and quality.
Most current development environments have good support for using Git.
In this sense, choosing a client is not something we actually need to do. Most clients work well enough, and the choice can be left to the preferences of those using the client. Many developers use the client integrated in their development environments, or the command-line Git client. When working with operations tasks, the command-line Git client is often preferred because it is convenient to use when working remotely through an SSH shell.
The one exception where we actually have to make a choice is when we assist people in the organization who are new to source code management in general and Git in particular.