You have 2 options for the backend:
a) home server - the harder way, depends on your technical specification. What functionality do you need from the server? For example Asterisk has audio-mixer for conference call, while it lacks user-presence (you need to integrate with Openfire).
Kamailio/Openser support presence through SIMPLE, but they lack audio-mixer support (you need to integrate with Asterisk or SEMS).
You can also consider "all-in" appliance like Sipwise, but it requires extensive knowledge if you want to configure something aside from the default configuration.
The good part is, most of the servers require very little effort to get the sip audio calls running, so if you only need that, better is to setup your own server.
The pros of this approach - you have total control over the service, you can view backend logs, you can test use-cases, which you can't with public service. The cons - it requires significant resource to setup, configure and support. This is subjective and depends on the functionality you need from the server.
b) public service - it's the easiest way. Depending on the service capabilities it maybe free or have a monthly fee. Most public SIP services allow sip audio calls, for everything else it depends on the service (calls to PSTN, video calls, conference audio/video calls etc). I would recommend sip2sip.info, but you can easily find others as well. The pros are you can start using it immediately (after you register) and you don't care about the administration of the service. The cons - you don't have control over the service, you cannot see backend logs (which are vital if you're developing feature-rich SIP software client).