According to Netcraft, something like 62% of the internet runs on *nix, which includes Solaris, Linux, and the *BSDs, with Apache as the web server. NT/2K running IIS accounts for maybe 29%. The rest are running Apache on various OSs including NT and Netscape Enterprise Server.
For stability and security, I would go with either Linux or FreeBSD (the most popular of the "free" *nixes). IIS, although easy to configure, continues to be a security nightmare and the costs for the OS need to be factored in as well.
Since churches are non-profit, go for something without cost - the free *nixes (*BSDs or Linux) and Apache. The *nixes all come with Telnet and FTP services (and you can install SSH if need be). You can also install stuff like MySQL as a database and even UBB (free version) for the BBS.
You can put all that you need together for only the cost of the hardware and pipe.