I am no expert on the topic, but I believe that a RAID 1 mirrored enclosure is perfect for my needs.
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As far as I understand it, if one disk of a RAID 1 mirrored setup goes bad, you are still good to go as long as the other disk is fine.
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I would like to get a 1 TB setup, cost permitting. If it costs too much, I would go down to 750 GB.
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Is it possible to buy two external drives and combine them into a RAID 1 setup through software?
First, you can do it in software, but you lose advantages over having a true hardware RAID, namely performance speed.
To address some of your concerns, have you investigated other RAID types, namely RAID-5? It is, in short, 'n' drives with one drives worth of parity information, distributed across all the drives. With a dedicated (hardware) RAID controller you get good performance plus data security because you can lose any one drive and still have your data.
RAID-5 is typically configured in 4 disk setups, so you get 3 drives worth of space, and 1 worth of parity. For 500 GB drives that gives you 1.5TB of storage space and the ability to save your data if any one of those four fail. You could do RAID-5 with less drives or more drives but there is a curve of how much space you gain (over RAID-1) and how safe your data is.
For instance, if you have 2 drives, you get 1 drives worth of data and 1 of parity; no gain over RAID-1. If you had 16 drives, you get 15 of data and 1 of parity, but now you increased your likelihood of drive failure four times that of a 4 drive configuration.
The beauty of RAID-5 over 1 is expandability; If your system supports more than two drives you can always start with 2 or 3 drives and upgrade later. RAID-1, even in a 4-drive configuration only gets you more data protection, never more space. (i.e., a RAID-1 array with 4 disks is only as large as your smallest disk, but it can handle 3 simultaneous drive failures)
Another option is RAID-0+1, a.k.a. "A stripe of mirrors" with 4 drives. Two pairs of drives are striped (data divided equally gives you better performance for read/writing), then you mirror one set to the other (giving you redundancy). In this configuration you can lose 1 or 2 drives and still save your data, so long as the drives you lose are not matched across the mirrors, if that makes sense.
You're right with all your research, but if you're really considering RAID, I'd go with something more expandable like RAID-5. There are a few NAS devices out there that work beautifully as 4-disk RAID servers, namely the Netgear ReadyNAS and the boxes made by Thecus, but both are fairly pricey. But you may save a little by getting less expensive disks too... You can find a 500gb drive for $99, but a 1TB drive is more than double that... So 2TB in 4 drives would be $400, but in 2 drives quite a bit more.
Just something to consider.