Hi,
If AppleGothic is there (it's absence is the most common cause of not being able to Access the Preferences) then Open Font Book again and use the "Restore Standard Fonts" item in the File Menu.
Messages store info in several .plists across several locations.
As the set up is new(ish) I would delete the lot.
In the Finder use the Go Menu > Go to Folder and type in ~/Library/Preferences in the dialogue box that appears (the leading ~ called a tilde, is very important.)
You need to find:-
com.apple.ichat.plist (the main one for the app)
com.apple.ichat.AIM.plist
com.apple.ichat.Jabber.plist
com.apple.ichat.Yahoo.plist
com.apple.ichat.Subnet.plist (this is for the Bonjour account but may not show if you have never enabled it)
com.apple.imagent.plist (this is a support app that provides a "listening" functions for Off line Messages of any sort once the app is set up).
Highlight then drag them to the Trash to delete them
and
com.apple.ids.service.com.apple.madrid.plist (this one hold the iMessages account info including linked ID and phone numbers)
com.apple.imessage.bag.plist (holds the current iMessages server info).
Now navigate to ~/Library/Containers/com.apple.soagent/Data/Library/Preferences
SOAgent is another Support app for the messages app (and FaceTime).
Most are Aliases in here except for some that start:-
com.apple.messageshelper.*.plist
Delete the set by Dragging them to the Trash as well.
Restart Messages

8:57 pm Thursday; February 4, 2016
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