Hmm...my team will probably be Typhlosion, Gyarados, Fearow, Gallade, Lucario, and Gliscor, so I'll probably have my Gallade or Lucario follow me around. I'm getting both HG and SS and plan on trading.
How do I get that team, you propose? Fly-by playthrough on one, probably using the One-Pokemon Challenge method (y'know, the one where you only use one Pokemon to beat the game?). After that, trade over the respective eggs (except in the case of Gliscor as Gligar can be caught in Johto) and then trade the eggs to the other game. Simple as that. :3