Yes, RAID 6 is the most resilient to failure (better than RAID 5 with a hot spare) and would thus be your best choice for true mission critical data. I mean the chance of you actually losing data on a RAID 5 setup is minimal, but if it's truly mission critical data than anything you can do to minimize that risk is warranted.

Big hard drives are comparatively cheap - I would suggest sticking in the largest capacity your NAS will handle, and do make sure the drives you buy are intended for use in a RAID array (many "green" consumer drives will not perform well and may even cause issues). If you can, try to swing the lower end of enterprise-grade drives... or at least something with a warranty longer than the stock 1 year.

I myself have a 6-bay ReadyNAS Pro server with 6 x 3TB drives in there (biggest I could get when I originally started building the array), setup as RAID 6. It originally started off life as 3 drives in RAID 5, but when I expanded capacity I bumped it up to dual redundancy. Also have an older WHS system with 3 x 2TB storage drives, which doesn't actually offer RAID, but has its own internal mirroring scheme for important data.

Haven't lost any of those drives yet, but I really don't ever want to lose my data - I've still got personal documents dating back to the DOS days and emails from the mid 90s!