Hi TRex and welcome to the confusing world of finding a suitable approach to handling Classical Music in Media Center, or any other media player
After reading about Tagging Classical Music in MC that is provided in the Wiki -
https://wiki.jriver.com/index.php/Tagging_Classical_Music you will probably, like me, realise that some of them Do Not Pay Due Respect To Classical Music and it's Composers. Plus some of them involve adding tags/fields that are badly named and could end up causing even more confusion than not using them could create.
However there is one which successfully manages to avoid misleading Tag Names, instead of using things like "Sub-Genre", "Classical: Title" or "[Classical: Opus]"
Instead it starts from the premise the Composers wrote "Compositions" in various types/musical styles "CompositionType" over multiple Classical Music Era's "Period" and that some of them may, probably most, contain "Movements" that have a "Movement Number" and "Movement Name".
It's the one outlined in this thread started by Wer -
https://yabb.jriver.com/interact/index.php/topic,128860.msg894607.html#msg894607 Unfortunately you will find that the vast majority of Media Players and Web Sites that provide Meta-Data were initially designed to only handle Non-Classical Music, with the inevitable result that Tagging and Organising Classical Music involves a lot of Time and Manual Effort.
So the first thing you should do is sit down with Pencil and Paper and decide/list just what information it is that you need/want MC to know/display to make selecting what to play as simple/easy as possible.
But don't be too pedantic about the fact that Operas and Ballets tend to use Acts and Scenes, or that Oratorios tend to use Parts, whilst Symphonies tend to use Movements; trying to provide ways of handling those apparently different category structures can appear to involve a lot of work, time and effort. Thankfully there is a way of simplifying that task by considering all of them to consist of "Movements".
Incidentally Wikepedia is a very useful source of information about what tags you may need to be able to identify what tags you may need and when you need to use them. Often it will have a page for each individual Composition listing things like it's Tempo and what "Performers" and/or "Instruments" are normally used for each Movement, Act, Scene, Part, etc. making up that composition.
For example the Album/CD Cover, Insert or Track List may state that the Orchestra, Chorus and Soloists are the "Performers/Artists" for every Movement of Beethoven's 9th Symphony, which is false/wrong because the Chorus and Soloists are only heard/performing part of the 4th Movement.
Unfortunately Wikepedia, along with a lot of the other web-sites that provide good, accurate and correct meta-data, only allow it's users to use cut and paste to transfer the relevant data/information to their Chosen Media Player.
Next you need to take a good look at what MC already has in respect of handling and tagging Classical Music to determine what additional tags/fields you need to add along with those views you may need to adjust/modify to suite your own requirements. You should also look at what other ways MC provides to allow you to organise and play you Classical Music Collection the way you would like to, a lot of users do it using Views, which tend to have a rigid structure but sometimes Smartlists with their Dynamic Structures are easier to set-up and use.
Then and only then should you embark on the task of restructuring your Classical Music Collection, by using things like re-naming and tagging, to get it to match your requirements.
In respect of basic tagging I do the the following:-
I always put the "Composer's Name" in both the [Composer] and [Album Artist] fields/tags - I place the Composer's Surname, plus suffix when needed, in the [Album Artist] field/tag and their full name in the [Composer] field/tag
For Box Sets I always use the Box Set Name for the [Album] tag/tag and place each CD's "Name" in the [Disk Title] tag/field.
By using information that is readily available on WikiPedia I use a combination of the "Artist", "Conductor", "Orchestra", "Chorus" and "Soloists" fields/tags to restrict the List of "Performers" to those who are "heard" on that track; i.e for Beethoven's 9th Symphony the Conductor & Orchestra's names are placed in the "Artist", "Conductor" and "Orchestra" fields for every track, whilst the names of the "Chorus", "Chorus Master" and "Soloists" are only present in the tags/fields for the 4th movement. I certainly don't need an Opera's full cast list as the Artists/Performers for a Track/Act/Part/Scene when it's only the Orchestra playing while the scenery is being changed.
I then use a Classics/Composer/[Album Artist] [Name] structure to rename/store my Classical Collection.
But the nice thing about MC is that you can use any storage structure you like when organising your Music Collection since its database/library knows where every track in that Collection is located and will find/play it whenever you want it to, provided the Track is currently available and not stored on a disc/device that is not currently connected to the PC you are playing your music from.