I have just finished developing a REST web service that is consumed by a mobile application. The web service is developed with Java and runs on an Apache server.
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Like I said, if it is for testing purposes you could always use a "normal" PC, running something like XAMPP.
As an alternative you could give RedHat's OpenShift a try, which offers a free, getting-started plan (more info here) that should more than cover your testing requirements.
To run your app (in Eclipse) you would need to : Run As -> Run on Server
And then select a server. If you haven't done so; I suggest you install a local JBoss/WildFly server (the wizard can take care of that for you).
Doing this will display options to run your app either on the local or the OpenShift/rhcloud server.This makes testing faster and allow you to avoid testing on the OpenShift live server.