RAID is really no better than having 3 external drives, unless you have a fourth and fifth drive to spare.
Failure rate can be mitigated in the way you are suggesting but if you look into the research this "mitigation" is in no way significant and relies on enterprise hardware to achieve even those middling improvements (ECC memory and Enterprise disks).
In the case of RAID 5, you'll want to keep two-three spares around - one hot-spare for your rebuild and at least a second for the inevitable rebuild failure. Mixing drives will not help much in this situation (it often leads to more problems here).
In the case of RAID 6, as you know, you're looking at three to four spare disks. Still, if one fails, you'll want to have a hot spare.
YOU DO NOT WANT TO RUN RAID 5 OR RAID 6 VIA SOFTWARE RAID. THIS IS A BAD, BAD IDEA AND SIGNIFICANTLY INCREASES FAILURES DURING REBUILD. You especially don't want to run an array (hard or soft) across different controllers.
Hardware RAID cards have dedicated ECC memory, battery back-up units, and their system is usually attached to a UPS - this is how they survive disk failures so well.
Point being that a proper RAID setup will cost a user a) $100 for a PERC + cables and BBU, b) $150 for a really low-end UPS, and c) not just three disks, but at least four (R5), if not five (R5+spare, R6), but, better, six (5 w/ two spares, 6 w/ one spare) or seven (6 w/ one spare). Then, if you choose to add capacity, you have to hope that your disk is still manufactured and buy another. THAT'S why it doesn't make sense for a consumer.
BB and other enterprises get away with RAID because they have 45 disks in an array in RAID50/60 or better. To match this sort of "security" for three disks worth of storage a user would have to buy 6-8 disks, plus some spares.
Even then, most data centers do not user consumer drives for all of the reasons above - if you want reliability, you pay for it. BB only uses consumer drives because they buy hundreds of disks at a time and are happy to throw them away after a couple of months.
ZFS, which is not software RAID, is an excellent middle-ground. While you'll want to pay for either ECC memory or a UPS, you don't have to buy a ton of disks at once, you can mix and match as you please, and you can add any disk at any time to any array whose controller has a port to spare.
BUT, all of this, still, is not a backup. Grab some external drives or an online backup service for redundancy because, eventually, disks fail!