Disk Mirroring

What OS are you going install?

Most operating systems have this built-in feature.   You don't need a RAID controller.   If you are using LINUX just use the md driver , and google syntax for mdadm to set it up.  
No matter what O/S you use, you need to make sure the BIOS in your computer is set up so that both disks are in the boot path.

The reason I am asking what OS is that the OS vendors do provide the software RAID.  They will work fine for a small environment but performance is slacking.

I would check the mainboard, as many boards do have a built-in RAID controller...

Otherwise it would depend on the OS you are going to use.

Linux has a very good Software RAID, I'd use that even if the mainboard's controller does have RAID, or at least if that controller is a soft- or fake-RAID controller. First of all Linux often doesn't have all to good support for those controllers and second, the Linux Built-in RAID usually performs just as good, and you can normally easily move the disks to another PC and it will keep on working.

If the OS is going to be Windows, it is better to use the controller's RAID and not Windows RAID, even if the controller is a fake- or soft-RAID controller.

it is going to be a windows machine..

I would use software like Acronis  Backup & Recovery to do image level backups of hard drive 1 to the Acronis secure zone, a hidden partition created by Acronis , on hard drive 2. This way when hard drive 1 crashes you can simply boot off the recovery CD and restore your image from the secure zone to the unpartitioned space on drive 2. You would be recovered in about an hour without ever opening the case. Plus you have the ability to do single file restores, something you don’t get with RAID.

Not all windows variations have software raid support, but here is a good tutorial that walks you through it.  
http://www.pcworld.com/businesscenter/article/132877/how_to_set_up_raid_on_your_pc.html