2nd Gen I beat all the Gym Leaders in Kanto. Now what?

So, I'm playing through Pokémon Gold, and I need some help.

I've beaten all 8 gym leaders in Kanto now, what's next? Do I rematch the Elite Four? Do I search for Red?

I haven't explored Mt. Moon yet, should I do that first?

You can enter Mt. Moon for the scenery, but apart from the new Mt. Moon square, and your 'rival,' there isn't that much to note. You would usually talk to Prof. Oak in Pallet Town to gain access to Mt. Silver via Viridian City, if you were in that place in the game, and then meet Red from there. Rematching the 'Elite 4' doesn't count for anything, but might be useful for grinding. Alternatively, you could look around for a shiny Pikachu.

Okay, thanks. Also, I can't believe I forgot to go into Prof. Oak's lab!