Essentially a run focused on getting money as quickly as possible. The goal being to buy the crown in the Celadon city Department Store which costs P 999,999 Might be an interesting Idea

There is a tm for payday, obtainable very early on, and the select group of Pokémon that can learn it include both Pikachu and Eevee. The problem with this is wild Pokémon are not fought in battle (with both lax, the birds and Mewtwo as exceptions, but those are all after you reach celadon anyway) which leaves trainers as the only option to farm money. And even then payday is best used when it's a KO option, especially as Eevee, who gets stab.

Also don't forget about the side quests involving obtaining sellable items (the pearl in pewter after poke-sitting a slowpoke comes to mind).

This really seems like it'd be one of those "Must Hate Self To Submit" runs where it'd just be hours of monotonous grinding. Since there aren't (to my knowledge) any trainers you can re-fight, there might even be an upper limit to how much money you can get without using Pay Day. Even then, Pay Day doesn't actually drop that much money. Each use drops only a few dozen P. Unless there's an easy way to earn a lot of money, it's not worth it.

Catch combos get you candies which you can sell for lot's of money, it's probably one of the best ways to get money.