So, the question is, is JRiver Media Center the right product for me?
Maybe. MC is more complex than itunes, but it's also far more powerful. Unfortunately, MC doesn't integrate into the Apple ecosystem very well. It runs great on Apple computers and works with all Apple music formats (other than DRM files). But there are limitations.
Should I buy a server license to install on the mac mini server and will that serve the whole "household" or must I buy a license for each unit?
Fortunately for you, MC's licensing is absurdly generous. One license allows you to install it on as many computers as you own within reason. The computers you described in your post would all be covered by a single license.
What is the best way to use and set up Media Center in my environment?
That's a very complex question that I'm not going to tackle.
Will Media Center totally replace iTunes and can I have playlists, also can I sync so that my playlists are available on iPhones and iPad?
Can I also put movies on the Media Center library that can be synced to the iPads?
In short, Yes, yes, no, and no. Sync with i-devices is spotty at best. There are workarounds, but they require a good bit of setup. I have not personally tried any of them. I no longer own any i-devices.
You can import playlists from itunes and/or you can build your own. Importing is a one by one proposition; that's not too bad if you have 30 playlists. It's bad if you have 300.
I will personally never go back to itunes. Why? Oh I'm glad you asked. :-)
1. Itunes pulls the rug out from under it's users, on average, once a year. That feature that you loved? Gone. Itunes just removes features willy nilly, and adds new ones that are weird and hard to use. There is no stability with itunes in this regard.
2. The look and feel change constantly, as per the above. Once you get used to managing your library in a certain way, they change it all around so that it looks "fresh and new and shiny", but then require you to relearn the basics. This is extremely frustrating.
3. ITunes thinks it's smarter than you and does all kinds of invasive crap under the covers like moving your imported files to different directories. MC never does these types of operations unless you explicitly tell it to.
4. Backups. Hey itunes, how do I back up my library metadata? "What's a backup?" MC makes library backups automatically every few days. You can make one manually any time you want. These backups can be used to restore to a point in time, or to move your library to a new system. ...and it WORKS! I've tested it many times doing different operations.
5. Itunes won't play FLAC. They invented their own mildly goofy lossless format for some unknown reason. FLAC is essentially the defacto standard for lossless music. I want to use it. So itunes loses here too.
6. Video (Music, TV shows, video clips, etc) support. Itunes is very focused on the ITunes Music Store for video. MC works with video from anywhere as long as it doesn't have DRM. It's also very powerful in it's ability to organize video.
I could probably go on, but those are the high points.
The good news about all of this for you is that MC has a fully functional 30 day trial. No limits, no removed features. It's 100% the same as once you buy a license. It just times out after 30 days and stops working. So you can test it "live" on your systems and decide if it works for you.
I think you'll like MC. I'm unsure about the best way to use it with many computers; that's outside of my current experience. But if you use Media Network with it, it might "just work" for you. In my limited testing, Media Network with one server and one client seemed to work pretty well.
Come back and ask more questions if you want.
Good luck!
Brian.