Hi,
.plists
Anything containing "iChat"
Some are less important as deleting them changes nothing about logging in.
For instance the com.apple.iChat.StatusMessages.plist only hold the most recent Status Messages you have set in Account that Have buddy Lists (AIM, Jabber.Yahoo and Bonjour i.e. nothing for iMessages.)
You might see a LSSharedFile one which is now useless as you no longer have the Menu item for it. It holds a list of the most Recent Chats. (it used to be in the File Menu). How many is controlled in System Preferences > General along with the setting for Recent Severs and Apps. (the "Documents" refers to the Saved items of Any app).
The com.apple.iChat.AIM( or Jabber or Yahoo or Subnet).plist refer to the Buddy List accounts you may have started up.
Jabber includes Google. AIM includes some Apple ID names (you add them as if they are AIM but use the regular password as AIM and Apple have an Agreement that their ID will be recognised an AIM Screen Names).
Deleting the actual com.apple.iChat.plist can help if the issue is with the Preferences and some Menu item Settings (Mainly Sorting Buddies and Chats)
com.apple.imagent.plist effectively logs in the accounts in behind the scenes when you start up the computer and provides a listening service to the various servers for Off Line Messaging.
If it sees a chat item it will start up the app (unless you set the item in the General section of the Preferences about setting the Status to Off Line when Quit)
This item only works for Accounts with Buddy Lists.
iMessages ignores this and still places number on the Dock badge but does not start up the App.
This is because as you have found out the iMessage account has no Status.
Deleting this .plist tends only to work with the Buddy List accounts.

com.apple.ids.service.com.apple.madrid.plist holds the Apple ID and the Alternatives you may have linked to it (iPhone Number(s) and other emails).
The com.apple.imessages.bag.plist only hold the server you were last connected to.
The com.apple.imessage.plist holds info about whether the default font has been chosen for Previews and the Font for the text has been chosen.
There are then some in ~/Library/Containers/com.apple.soagent/Data/Library/Messages
You have some here that have "messageshelper" in the names.

Most of the info though is about Buddy Lists Accounts.
Back in /Library/Preferences and just below the madrid one there are many IDS items relating to the links between iPhone and Mac for both messages and the FaceTime app, depending how and which functions that are connected for.
Keychain Access will show you an IDS: yourAppleID-Auth Token This may have to be removed if the Migration has copied across one from another Mac.
It is this bit that holds the info used based on it's creation by having the Mac's Serial Number. That is to say that the ID and Password and the Serial Number are used to help create this token when logging in the first time.
Migrating the Keychain from another Mac brings a token with the wrong Serial Number in effect.

9:27 pm Saturday; December 24, 2016
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 10.x and an iPad (2)