If you don't want to use Title as Title, you typically rename it to something more contextual to what the list is storing so you don't lose the link to item with edit menu control block.
As you've indicated, hiding the title field negatively impacts search and makes it more difficult to edit items. You can try setting another field to be the title field, I've done that in the past with mixed results.
See https://msdn.microsoft.com/en-us/library/office/microsoft.sharepoint.spfield.listitemmenu.aspx and https://msdn.microsoft.com/en-us/library/office/microsoft.sharepoint.spfield.listitemmenuallowed.aspx.