Welcome to the game!

Glad to hear you like the fluffs you have so far.
The next event for pulling eggs will be our Homecon this weekend. As for tips, if you're after a cat or dog look for "natural" colors rather than bright blues/reds/etc. But beware! Brown eggs can also be things like tunnelers or moss hoarders.
Dog/cat wyrms are in the uncommon bracket of eggs if that helps? They've got complex paint jobs so they tend to sit in the batches of uncommon/rare eggs at conventions to make up for the extra time and effort that goes into them. Birds too.
Generally a good tip is just what Mel said, though! Find an egg you think is beautiful. Sometimes you'll get a big surprise what you end up with. (Some eggs are 'dummy' eggs from time to time.)