Need both a Readable Secondary and High Availability
@sp_BlitzErik is correct.  AGs need planning and care.  AGs don't have the particular issues you struggle with in Transactional Replication, but they have others.

If you are comfortable with Windows Server Failover Clusters (WSFC), then you have conquered the biggest hurdle to deploying and running a SQL Server Availability Group.  AGs use WSFC for the quorum model, and for a floating IP that moves between the nodes.

If you are willing to not have automatic failover, you can use the new "Clusterless" AGs in SQL Server 2017.  See Read-scale availability groups.  They are called "Read-scale" AGs to emphasize that they are not intended for HA, but they do support synchronous (zero data loss) replicas, and manual failover.


  
    For a small shop with no DBA, what solution(s) should we consider?
  


Also must mention that Azure SQL Database is ideal for a small shop with no DBA.  And enables you to create readable replicas in the standard tier, and premium tier databases get an automatic readable replica.