Electronic – How to pick a surface mount LED

if all your LEDs are being controlled from the same source, consider using a microcontroller + differential Manchester encoding + your high/low LED states to encode bitstrings of repeating sequences like:

id #0: 1000000000000000[10000000000000001000000000000000....]
id #1: 1000000000000001[10000000000000011000000000000001....]
id #2: 1000000000000010
id #3: 1000000000000011
id #4: 1000000000000100

to encode ID numbers as a 16-bit bitsequence consisting of a 1, then 7 zeros, and an 8-bit ID#. Then when decoding, look for a 1 followed by 7 zeros, then take the subsequent subsequent bits. This works for all 8-bit ID#s (even #128 = 10000000 which encodes as 1000000010000000 which can't necessarily be synced properly but for that number it doesn't matter).

(If you have fewer potential LEDs, use fewer bits; this scheme is pretty simple and generalizes to a 1 + (N-1) zeros + an N-bit number)

Manchester encoding is self-clocking so you should be able to synchronize a receiver to it (even if it's another microcontroller not sure of the frequency, sample several times per bit so you can stay locked).

Diffusers are very inefficient ways to spread light at a wide angle. Proper optics can do this with much less loss.

However, if you really want to use the ping pong ball diffusers, one or more surface mount LEDs without lenses will probably be the best. LEDs in 0603 package tend to be the cheapest, so you can compensate for lower overall emission (and the loss introduced by the diffuser) by using multiple of them. A cluster of three or four 0603 LEDs under the ping pong ball should provide more even light, at a wider angle, and still cost less than the archaic thru hole LED you reference. They will cost even less when you consider they can be machine placed.