for the togepi egg, you need to save before you get it. After you've gotten it, it's values, including shiny-ness are set. I'd recommend trading over a flame body pokemon or getting a slugma from primo to help it go faster.
my johto starters came insanely quickly. I got Cynda on one HG file after less then 100 SRs, Chiko on SS after 500 and Toto after about 450 SR's on a different HG file