Well, actually, if you have a RAID1 system implemented by software (as opposed to a RAID controller card) you will get increased overhead when writing because it has to write the data N (three) times. You will also only get performance INCREASE if your configuration supports split seeks, otherwise it won't make any difference.
The primary purpose of RAID 1 is the R in RAID: redundancy. It provides fault tolerance, but is not designed to improve performance. If you want fault tolerance and improved performance, choose RAID 3 or 5.
Choose RAID 3 or 5 will will also net you more space: RAID 1 mirrors data on all drives, so N times 500 GB drives will always give you 500 GB of total space, because the other drives are just copies. RAID 3 or 5 will give you N-1 x SIZE as long as they are all the same size. So, 3 500 GB drives will get you about 1 TB total space (as the space of the third drive is used for parity calculations).
RAID 5 would be best for you, probably, since it splits the parity among all three drives, whereas RAID 3 uses the Nth disk to store all the parity.
I use RAID 5 on my network file server.