How to chose a diode for breadboarding?
That one will work. Alternatives are 1N4148, 1N914, 1N4001 (or 400x). 

Your application is for low frequency, and the differences between diodes won't have much impact on your system. You are correct that choosing one with a higher voltage and current rating is appropriate.

Note that if you can't obtain one, using an NPN transistor will usually work -- connect the base to the emitter, and use that as the anode ('+'), and use the collector as the cathode.