Pokémon Trading Card Game/Fighting Club

The Fighting Club acts as the game's one real "quest", which requires possibly revisiting locations you've already been to accomplish a certain goal. Upon first entering the main area of the Fighting Club, you'll find it strangely empty, with only Leader Mitch in attendance. He tells you the following when you first speak to him, which sets the event flag:

Until you actually defeat all three of his pupils at the clubs listed below, he will continue to repeat the last three lines. Upon defeat each member of the Fighting Club will return, and once all three return you will be able to challenge Mitch.

Much of the advice from the ../Rock Club/ holds true here since Fighting, Rock, and Ground are closely related in this era of the TCG. It's rare that the Fighting Club members are going to be able to exploit your weaknesses unless you're using a Lightning / Colorless deck, and their decks are highly unlikely to feature resistance to most of your deck.

Deck Building Strategy
Flying-type monsters (Pidgey, Pidgeotto, Pigeot, Farfetch'd, Zubat, Golbat, Doduo, Dodrio, etc.) all have resistance to Fighting/Rock/Ground monsters, as you would expect from the type matchups found in Pokémon Red and Blue. One card you may find an oddly effective stall, though, is Gastly Lv. 8 - in spite of how it's a pretty useless card anywhere but here and the Rock Club. While it only has 30 HP, it also resists these attacks for -30 damage. Add to that the fact that Gastly Lv. 8 has the Sleeping Gas attack (Flip a coin - if Heads, the opponent is now Asleep), and you'll be able to stall out most of the Fighting Club's star monsters until you can get enough energy on your Bench to act. Gastly Lv. 17, boasting 20 HP extra and Lick for 10 damage, is more effective at whittling down your opponent. Either version of Haunter will stall, but Lv. 22 can put an opponent to Sleep without a coin flip and then do 50 damage the next turn with Dream Eater. Gengar is a possible choice as well if you think the more reliable Dark Mind — 30 damage to opponent + 10 to one benched monster— and Curse — Move 1 damage counter (10 HP) per turn — is going to be better than risking the opponent passing a Sleep Test to do 50.

Chris
Chris is in the lounge of the ../Rock Club/. He'll return to the main hall of the Fighting Club after defeating him.

Michael
You'll find Michael in the lobby of the ../Grass Club/. He'll return to the main hall of the Fighting Club after defeating him.

Jessica
Jessica is hanging out at the card table in the lounge of the ../Fire Club/. She'll return to the main hall of the Fighting Club after defeating her.

Club Master: Mitch
All members of the Fighting Club must be fought in alternate locations before they will return to the Fighting Club after first speaking to Leader Mitch. Leader Mitch cannot be challenged until this quest is completed.

Coming to the Fighting Club first and speaking to Mitch before you get started on any other medal can save on some backtracking. In a game where you're likely to be grinding to get that one card you want for your deck, this can be a major boon.