Mega Man 3 is when the bosses get much harder, in my estimation, so the battle order becomes more important and less of a convenience than it is in the first few games. But there are goals: Rush Jet is useful before Hard Man, and Shadow Blade is handy all around. But mostly I just want to fight a boss I can beat and then use the vulnerabilities all around. Oh, and the Top Spin has a bug which would be annoying to hit later in the game, so that only doubles the desire to have Shadow Man early. So…
Top Man (Buster), Shadow Man (Top Spin), Gemini Man (Shadow Blade), Needle Man (Gemini Laser), Snake Man (Needle Cannon), Spark Man (Shadow Blade), Magnet Man (Spark Shot), Hard Man (Magnet Missile).