What file system format suits best in this case: ext3, ext4, xfs or something else?
Most likely either ext4 of xfs. Format it each way and test your workload.
I tend to not use RAID 1.
If you don't give a single shit about availability, then fine. If you do, I'd reconsider this approach.
format one disk to be devoted to mysql and the other to the rest of the filesystem. I think this would minimise disk i/o delay and also reduce the write cycles, so enhance the overall life expectancy of disks. How do you evaluate this approach?
If the only server process running on this is mysql, there's not a ton of benefit to running it on a separate disk. If it is a server that runs apache and other processes as well, this makes a bit more sense. There will be slight performance gains by putting it on a separate physical disk, but I honestly would run the disks in RAID 1 ten times out of ten.
Seriously, though. If you care one bit about the users of the server, it's negligent to not run RAID. Think about it like this:
How frequently do you take backups? If it's daily, imagine that a disk dies right before the next backup window. How would your users react to losing a day's worth of work?
Now imagine that it takes you 4-6 hours to restore from backup, test, and bring everything back up. Now your users have lost a days worth of work and haven't been able to use the server for the better part of the day.
Is it really worth the slight bit of extra performance? Probably not.
If you really want to separate your DB, get two more SSDs and run two RAID 1s or a single RAID 10.