I believe Akkadian would fall under the Semitic Group, however it is a member of the "East Semitic Language Group" (what would be Family in ArM) which all died out some near 2,000 years before the standard AM start date. That would classify it as a Dead Language and so it would have a Use Type rather than Dialects.
So something like:
Group: Semitic
Family: East Semitic (or pick something else, all of these died out millennia before AM)
Language: Akkadian, Eblaite, Kishite
Dialect: [Use Type]
Sumerian is a 'Language Isolate". In fact it is one of the oldest recognized language isolates. Since it is the only language in its Group it would be pretty easy to classify.
Group: Sumerian
Family: Sumerian
Language: Sumerian
Dialect: [Use Type] (it was used as a Classical Language for learned persons till about 100 AD)