Hi,
I will endeavour to explain how they got into this mess as this leads to some clarity about what can be done with which accounts.
Basically this is a small essay to explain 15 years of history.
Messages can use accounts that use five services.
Original iChat (ver 1 and 2) was an AIM only client for External chats and had the then Rendezvous (No Bonjour account) for LAN chats. At version 2 it could do Video and Audio Only chats.
iChat 3 added Jabber (this now includes the Google Talk server and Facebook chat accounts)
All of these (now up to three accounts types) can do Video and Audio Chat.
Screen Sharing is added in iChat 4.
iChat 6 (Lion) add a Yahoo account ability.
However this is only a Text based version.
It also uses a different plug-in mechanism to the ones that run AIM type, Jabber type and Bonjour accounts.
Version 6.1 was in fact Messages beta which ran from May to Dec 2012.
Version 7.0 becomes the full on Messages app.
It has all the four types of previous accounts and adds the iMessages account.
Obviously at this point the whole interface changes and so does what Messages asks you to fill in as the "first account".
The iMessages and Bonjour accounts can only be disabled and not removed from the List (in Messages > Preferences > Accounts).
Obviously the Apple ID can also be removed from the iMessages details as well.
How accounts with certain places can already be in the Preferences > Accounts
If you Upgrade from Lion or Snow Leopard you may already be using a Google Email account or a Facebook connection or even a Jabber email.
These will get added to the Mail, Contacts and Calendar System Preferences Pane.
They may also get Enabled for Messages.
So after you add your Apple ID to "register" with iMessages the Messages > Preferences > Account may show more accounts based valid AIM, Jabber and Yahoo IDs.
Names and IDs valid as Messages accounts
Ever since Version 1 of iChat Apple have had an agreement with AIM that Apple IDs issued by Apple will also be valid as AIM Screen Names
Over the past 15 years that has acquired some history to it as well.
Firstly were @mac.com names. These worked as Paid For accounts, Account that were Trial accounts even after the Trial finished and any account that was paid for but lapsed.
These were issued under the .Mac Service that Apple did back then.
Secondly Apple changed to MobileMe.
Trial accounts worked only for the Trial period and paid for accounts worked only during the time they were paid for. These ended @Me.com
However... During this period Apple Continued to run an @mac.com "iChat Name" registration page were you linked an existing email to an @mac.com ID to us as a AIM Valid Screen Name in iChat - rather than registering with AIM.
Obviously more recently Apple did away with Paid For services and went to iCloud.
The change initially gave you iCloud Issued @Me.com (it seemed it was moved server as an iCloud account) and then later @icloud.com IDs
This means if you have not updated an @me.com account form the MobileMe period to be an iCloud account it will not work.
There are two NOTES for these accounts
1) AIM limit their passwords to 16 characters so you must as well for these Apple IDs.
2) iCloud registered Accounts (@me.com and @icloud.com) will not work on iChat 5 or Earlier due to a new security check the later version make.
Jabber Accounts.
This is a non centralised service based on various server working together.
Many take the form of UserID@jabberserver.com
However Facebook and Google also run Jabber servers.
Google's is based on direct Google Mail IDs.
However there are two forms of these (@gmail.com and @googlemail.com) which means there is a server name issue that is got around by there being a separate option to Add Google accounts (the server is called talk.google.com)
Facebook issue you with a "Chat" ID after you have Enabled "chat" on your Facebook settings.
It adds the word Chat into the ID.
Yahoo
Whilst using their own Yahoo for Mac you can use any of the IDs that Yahoo have allowed to be your Account in Messages it can only be an Yahoo account itself.
However your Buddies in this account can be all type that Yahoo support.
Interservice compatibility
Whilst at AIM (web pages) you can add Google and other IDs to a Buddy list and have similar AIM Buddies to a Google Buddy list at Google the accounts within Messages (or the earlier iChat versions) cannot connect to each other.
This means it is AIM to AIM or Jabber to Jabber etc.
As the naming format looks like email IDs it is possible to actually add a Google Buddy for example to a AIM Buddy list and of course vice versa. However the Buddy will either not show up or look Off line all the time depending on the Service/Buddy list type.
iMessages is to iMessages capable Macs or iOS devices only.
The Mac version though will not send SMS instead (it does not have a Phone Carrier to fall back on.)
The iMessages account invokes FaceTime if you use the Video icon that appears top right in a Chat/Conversation.
Only the AIM and Jabber plus the local LAN based Bonjour account can do Video and Audio Chats.
It takes an account that can do these to do Screen Sharing.
Screen Sharing is actually an Audio Only chat with a VNC connection running alongside that provides the "pictures" of the Desktop at the other end.

8:11 pm Monday; April 14, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad