SQL Server DR, mirroring or virtualise and mirror
I would implement Log Shipping, which is just a process of taking transaction log backups at one site, and restoring them at another site. This operates at the database level, and it will inherently handle all the schema changes because backups operate at a level above that.

There's really no other sane solution on Standard Edition because the requirement of having an asynchronous process severely limits the available options. (If you're just getting started in this area, don't even think about any kind of SQL Server replication.)

Note also that as far as I can tell (and I could be wrong about this), Windows Server 2012 storage virtualization (aka Storage Spaces) is meant as an enhanced RAID controller given a set of local disks; it's not for replicating virtual machines across data centers. I believe to do that requires specific storage hardware that supports it, and I don't think you're looking to go down that path right now.


  I dont want to put much more stress onto the SQL server as it is quite busy with both reads and updates.


Quantify this. What kind of options do you have to upgrade the hardware (I'm assuming it's several years old at this point)? Is the bottleneck CPU or I/O?

Regardless, if you're legitimately maxing out the available resources right now, virtualizing is a bad idea, as it adds inherent overhead to the system. Virtualization is great, and it may be appropriate here for other reasons, but definitely not if you're concerned about performance on your current physical hardware.


  I don't want the primary server waiting on the secondary server to update before it commits a write.


I'm assuming this is because there's a slow link between the sites? If that's the case, and you want to protect against hardware failure, consider implementing a synchronous site-local mirror (on a separate physical box using Database Mirroring) for high availability, and then an asynchronous remote site using Log Shipping for disaster recovery.

Any kind of mirroring or replication is going to add some latency or load to the primary server. How much depends on the hardware and the workload. This is the tradeoff you have to make to protect against failures. It isn't completely free, but with proper hardware and design, it can be minimized to the point that it's irrelevant.