Pokemon-go – How does Pikachu riding on your shoulder work

As far as I have experienced the only order of eggs is whether or not they're currently incubated (and their chronological order), since they're on top of the list. The rest is most likely random.
The (non-incubating egg's) order might even change when you pick another egg to incubate or get one to fill an open slot. This leaves only two possibilities:

• Random order
• Fixed order, but this means the setting determining the sorting order changes when you start a new incubation (contained Pokémon for example) ...which is very unlikely.
  This would mean, if they're sorted by ID the contained Pokémon changes every time the amount of eggs changes. Or the IV, or Level, etc. To be honest, that would be stupid programming since they'd be trying to randomize the order and could simply use a pure randomizing algorithm instead.

If it is rare, catch it anyways because

• You may not get another chance to spot a wild one
• You may not necessarily hatch the same wild rare pokemon later on.
• Sometimes wild pokemon can appear with excellent IVs (but appear weaker due to lower CP)
• You get extra candy for power up
• +100 Stardust... why not?
• You will own two strong rare pokemon to use in gyms (What's better than one strong snorlax? Two strong snorlax's!)
• Bragging rights

What's to lose?

• Some balls, berries and time. The latter I agree time is precious, but the rest are not limited resources, e.g you can always get more balls and berries.

In terms of catching any pokemon rare or not, if you plan to conserve your items, I would avoid catching Pokemon that aren't weak or strong, the "so-so" ones.

Weak pokemon are great because they are usually easy to catch, which means easy stardust and candy, and more pokemon to do lucky eggs. Strong ones might be useful for battling and won't require as much candy and stardust to power up. The one's in the middle are not ideal for any of these usages.