Standard Edition High Availability without Shared Storage
As per this BOL reference, here are the only options you would have with Standard edition:


Log Shipping
Database Mirroring (sync/safety only)
2-node Failover Cluster Instance


Because you don't want to use shared storage between different participants, that would automatically rule out the failover cluster instance, leaving you to choose between log shipping and database mirroring.

Those are two very different solutions, with two very different needs driving them.  What are your requirements for failover?  Reporting?  How many copies of the data do you want?  Until those questions are answered, you wouldn't be able to choose between these two rock-solid solutions.

EDIT

I must have completely missed your requirements in your question, but with Paul's excellent edit and graphic there, it seems as though a lot of the requirements are already there (although you don't seem to point out reporting or warm data, so I'll assume that's not necessary).

Physical Separation
You could get yourself into trouble here with database mirroring if you're talking about cross-datacenter or geographic separation type of distance, as the restriction for only sync/safety mode could introduce performance implications.

Failover Tolerant Application
Unless you have the logic in your application, log shipping wouldn't be able to help you here.  With database mirroring, depending on your provider and capabilities you could specify the failover partner though.

Failover (preferably automatic)
This an easy one.  Log shipping doesn't have this capability, you'd have to manually intervene.  Database mirroring would be able to fulfill this.

No Shared Storage
Both of these solutions do not require shared storage.

Must work with EF
I don't see why EF would have a problem with database mirroring, but I couldn't say for sure on this without doing more EF research.

SQL Server 2014 Standard
If you mean Standard edition, that is answered above.  If you mean "standard" as in "current", then database mirroring is currently deprecated for what it's worth.