I almost always start with the fire type. The other types are usually encountered fairly early in the game, while the first fire-types are usually a lot later on.
I mean, in my game right now in HeartGold, my team consisted of Quilava (fire), Flaaffy (electric), Butterfree (bug/psychic), Bellsprout (grass), Wooper (water/ground), and Pidgey (normal/flying) before I even went to the first gym. That's right - I had ALL of the basic types covered right away, before I even got my first badge.
The fire-type is almost always the best choice to start with. You should usually wait to get the others later through trading, if possible.
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