What User Level is needed for Transactional Replication
The Snapshot Agent process account used to connect to the Distributor must be db_owner in the distribution database and have read, write, and modify permissions on the snapshot share.  The account used to connect to the Publisher must be db_owner in the publication database.

The Log Reader Agent process account used to connect to the Distributor must be db_owner in the distribution database.  The account used to connect to the Publisher must be db_owner in the publication database.

The permissions required by the Distribution Agent process account depend on whether you are using push or pull subscriptions.

For push subscriptions, the Distribution Agent process account used to connect to the Distributor must be db_owner in the distribution database, be a member of the PAL, and have read permissions on the snapshot share.  The account used to connect to the Subscriber must be db_owner in the subscription database.

For pull subscriptions, the Distribution Agent process account used to connect to the Subscriber must be db_owner in the subscription database.  The account used to connect to the Distributor must be a member of the PAL and have read permissions on the snapshot share.

The is all covered in the section Permissions That Are Required by Agents in Replication Agent Security Model.