Be aware that there are arguments about whether BTRFS is really ready for serious use yet. For me and for my requirements, I think that it is and I’m preparing to do some exploratory work with it, but there are others who will tell you that it isn’t ready.
What would you lose if it did go badly wrong and how valuable would it be to you?
I’d guess that we can presume that the 3TB drives are faster and that you would rather use them for most things, simply because they are newer and bigger?
Is RAID RAID-like enough for you?
The ‘old-fashioned’ way would be to select a filesystem like ext4 and use the multi-disk driver to make a raid array. The ‘more modern’ (and, for more modern you can read ‘not as fully debugged’, or ‘available with extra excitement’ if you like) is to use something like BTRFS (and the only other thing sufficiently like BTRFS is ZFS - ZFS, in general, is more mature, and there are two Linux implementations, both of which are somewhat questionable (licensing, speed, maturity-of-implementation) but could be the answer in the short-to-medium term); ZFS/BTRFS incorporate the ‘making a RAID array’ part in with the filesystem set-up, so you no longer need the multi-disk driver to stitch together partitions into a raid array.
It all depends a bit on what you are realistically trying to protect against (and, if a fairly well populated drive goes south on a big RAID array, remember that the rebuild time could be significant - so, if immediate availability, even with one drive down is your thing, you might not be getting that because with the array degraded the performance may not be sufficient for you to feel that the system was actually ‘available’, even if technically it was ‘available, but slow’ - more of an issue with RAID 5/6 rather than 1 (or 0, for that matter, in hybrid modes such as 10, but we are getting ahead of ourselves), but do be realistic - even the best system will struggle to give you ‘so you wouldn’t notice’ performance all throughout the problem!
I take it that you have enough SATA (or whatever) ports for the number of disk drives that you want to connect.
(sorry, DJH replied while I was writing this - must get my fingers upgraded!)