One I just thought of is Mono-Bug for Heartgold. It could be really good; this game has some really good bugs out there. What I'm thinking of is:
-Butterfree
-Heracross
-Scyther
-Scizor
-Pinsir
-HM slave
As you can see, you can have a full team before the third gym. This would definately be easier on Heartgold; Butterfree is better than Beedrill. Falkner shouldn't be a problem; Raise a Butterfree and grind it to level 12, get sleep powder, and defeat his team. This is made easier in HGSS by the fact that none of his Pokemon have Physical Flying moves, so Butterfree should be able to stand up to them. Bugsy might be difficult, but again, a well-played Butterfree could get you the win here. Whitney will not stand a chance; either Heracross will sweep her or you can go for a team effort using Scyther and Pinsir as well. You can catch two Scyther, and evolve one into Scizor; The Metal Coat is available from the Pokeathlon Dome on Fridays, so you bcould have a Scizor before Morty. Speaking of Morty, we have another easy battle. Butterfree's Psychic attacks will be your friend here; Scyther and Scizor's Technician-boosted Wing Attack and Metal Claw should wreak havoc. Next is Chuck; No contest for Scyther and Butterfree. Jasmine is best dealt with by Heracross and possibly Pinsir, while Pryce can be destroyed by the former two plus Scizor. The hardest battle would definately be Clair; Gyarados and Kingdra spell trouble, but you have a bunch of powerhouses so it should only take a couple of tries to win. Also in Blackthorn is the abilty to get what he is famous for; the Technician-boosted Bullet Punch! Anyway, the Elite Four. Will loses to pretty much your entire team, except maybe Heracross, Koga will require some effort, Bruno loses to Butterfree and Scyther, Karen has no chance, but Lance could be really hard; watch out for that Charizard!