After searching for a bit, you come across a round pink pokémon.
Speed 2+ beats it, so I'm fairly certain any of your mons would go first.
Hatch times for eggs, as of 4AM:
Starly: 4.96 Days (119 hours)
Eevee: 17.9 Days (430 hours)
Sandshrew: 6.4 Days (154 hours)
Gible: 20.75 Days (498 hours)
Joan looks at Collin with an annoyed expression. "You're asking for a battle now? Medical supplies are too scarce for that, and I'm not sure if you've heard, but we were attacked while you were gone yesterday. Steve died in the attack, but we were able to hold them off. I can't be battling so soon after that just for a challenge."
Not much to say here. Hatch time for the Meowth, as of 4AM:
Meowth: 7.25 Days (174 hours)