OS X Server includes Mail and Calendar server software. It's compatible with all the kinds of computers you listed. It is not 'Outlook', however, it's real Mail and CalDAV and talks to real Mail and Calendar software.
It's as dependable as most server software. Without knowing what your problem was with your Linux server I can't say more. For all I know the real problem was your network hardware.
OS X Server is not a replacement for a full-on Microsoft Outlook environment; particularly not if the local folks are using Outlook for what it can really do. For that, you really need Windows Server and Exchange and Sharepoint and related Microsoft products.
OS X Server calendar services provides the CalDAV standard, which may not be compatible with your Windows clients; you'll want to research that, as you may need to acquire different client software or plug-ins.
If you've previously been using Linux servers, then OS X Server does provide similar capabilities; it's based on Postfix, Dovecot and related servers. There are Windows clients that are compatible with the protocols, though Outlook generally isn't one I'd recommend here. (Not that Outlook is bad. It's just really intended as the front end for Exchange Server and related.)
There are also (larger) hosting providers around, which may provide you with what you need here, without having the overhead of your own hardware and network support. OS X Server is easy to manage in comparison with other servers I've worked with, but it still assumes some experience and knowledge of IP networking, DNS services and some troubleshooting when the server or the local network or the gateway-firewall or your ISP link goes sideways. There's no free lunch here.
There is now level of Office 365 which includes a hosted MS Exchange service as well. You can then use Outlook for Mac, ActiveSync on iPhone, and Outlook for Windows to connect to this service.
If you want to run your own on a Mac, then the nearest option is Kerio Connect.
Outlook does not support caldav and carddav, but now it's possible to sync with os x server with EVO Collaborator for Outlook 2007~2013
it enables outlook to use carddav and caldav protocols to connect to MAC OS X and sync with user's calendar and address books
simply close outlook and install it, and open outlook, goto EVO tab, click profile button, and add a new profile, note that the HOST url for Mac OS X Server is https://serverIP:8443/