Hi,
Jabber is the only remaining Buddy List account.
AIM stopped in December 2017 and was removed From High Sierra as it was published.
Yahoo was stopped by Yahoo then the app totally rewritten and Apple have not dded it back to Messages.
For some reason Bonjour in Messages was also stopped.
To Add Google to Messages create the account in Internet Accounts as a New Account > Other > Messages and select Jabber.
In Sierra you had to add the Google Account to Messages First then Activate Mail in Internet account as they used different servers and the OS coped adding them this way round.
Adding to Messages first in High Sierra causes issues with the Buddy List not displaying properly or not allowing the Account to Send messages.
Back to the iMessages account issue.
The Mac should have used an Apple ID that was iCloud Valid.
It can then send and Receive at the Apple ID.
Then the iPhone has the App Enabled and after the number is verified then it can sent iMessages to and from the iPhone number.
IF SMS is also turned on in the app it can Send and Receive SMS.
Adding the Apple ID to the iPhone links them to sync iMessages between the two IDs.
Next the iPhone has to be on the same LAN as the iPhone.
Enabling Text Forwarding at this point will normally cause a pop on the Mac that Shows your a Code Number that needs to be entered back on the iPhone.
It is on adding a second device that your see the drop down list of devices such as an iPad using iMessages with the same Apple ID (or an Apple iPod Touch).
IF the Mac is the second device and then if it does not show up, it and the iPhone are not on the same LAN.
Other possibles are that either the iPhone is not logged in to iMessages with the iPhone Number (rare but possible) see Send and Receive; the number should be ticked.
Or the Mac is not logged in using the Apple ID.
Test by restricting the Mac to just using the Apple ID in Receive At. (The Send From drop down will disappear)
On the iPhone deselect the Apple ID so it can only Send and Receive from the iPhone Number.
ON the Mac start a new Messages and manually enter your iPhone Number including Country Code.
Send the iMessage.
If the iPhone does not get it then the Mac is not logged in properly.
If it is not work though this Users Tip When the iMessages account will not Login
8:47 pm Sunday; January 7, 2018
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)