Relay kickback diode selection

What criteria should be considered when selecting a kickback shunting diode for a relay?

Until now I have just grabbed a 1N4001. Unfortunately when I went to the drawer I found it empty. Which has made me consider why have I been using it, what criteria should be involved in the selection, and what other alternatives that I have on hand would work. 1N914? 1N4148?

PIV > 2 to 3 x the coil voltage. ( The diode is forward biased during the surge)

If relay switched occasionally, then the Non-repetitive Surge current rating > than relay coil current. (1N4148 will likely work)
If relay switched rapidly, you might consider that the current rating should be closer to the 60Hz repetitive peak current rating...

I typically work in the 5-24VDC range or 120VAC. Even the 1N914 has 100V PIV and a surge current of 1A. I would never have considered using it until I asked the question.

If the coil is AC, then you can't use a standard diode. Two back-to-back zener diodes or a bi-lateral surge suppressor of the appropriate voltage rating will.

I know that. I was just listing the relay control voltages I typically work with. I'm still stunned how over rated my diode choice has been.