As stated previously, there is no perfect CI tool that will suit every project or, most importantly, every organization and workflow it uses. I can give only a single suggestion for open source projects hosted on GitHub. For small open source code bases with platform independent code, Travis CI seems like the best choice. It is easy to start with and will give you almost instant gratification with minimal amount of work.
For projects with closed sources, the situation is completely different. It is possible that you will need to evaluate a few CI systems in various setups until you are able decide which one is best for you. We discussed only four of the popular tools, but it should be seen as a rather representative group. To make your decision a bit easier, we will discuss some of the common problems related to continuous integration systems. In some of the available CI systems, it is more possible to make certain kinds of mistakes than in others. On the other hand, some of the problems may not be important to every application. I hope that by combining the knowledge of your needs with this short summary, it will be easier to make your first decision the right one.
Let's discuss the problems in the next sections.