The typical scoring strategy is to focus purely on 2 stats, (e.g. Vocal/Dance) with a character that has a burst for the 3rd stat. So for my example, Miki is a good character for Visual burst. Burst scoring is based on your danketsu value (hidden within the game).
Ah right, the burst score depends on danketsu, that was the piece i was missing to make sense of what i was remembering. Let's say you focus on visual, then your secondary stat is dance (the one to the left of your focus), and you dump vocal (the one to the right of your focus). At the beginning of a song, you use your secondary appeal to boost the multiplier of your primary appeal to 1.5, and then you use your primary appeal a few times until it drops to 1.46 or 1.45, and then use your secondary appeal once to get the primary multiplier back to 1.5.
Iirc i kept using the primary appeal for a bit when a burst was coming up without raising the multiplier again. When the burst is ready, use it, with an idol with as many appeals in your dumped stat and as few appeals in your secondary stat as possible. The reason for this is, that the score only depends on the multiplier and danketsu, the fact that you dumped the third stat doesn't matter at all. By that time the multiplier for the dumped appeal will definitely be maxed (and doubled during the burst), and the multiplier of your secondary stat will be really low. If your dumped stat is vocal, then Chihaya is the best idol to burst, Miki for visual and Hibiki for dance.
After the the burst, your mulitpliers will be in a bad spot. For example for Chihaya (PS3 version) they will be 0.9 dance, 1.0 visual and 1.2 vocal. So your secondary stat is already quite low, and the dumped stat you are not going to use anway is already at 1.2. If you use a memory appeal right off the bat after a burst, you reset all the multipliers to 1.1, so you can raise dance and visual, and the loss in vocal doesn't matter at all (it will be 1.5 anway by the time you burst again).
Oh also I just remembered something I was curious about: In the begginers guide on the wiki http://imas2.wota.info/strategy/beginners-guide it says for your third and fourth song "choose a personal song of one of the members of the unit and, if possible, one which does not match your specialisation." and I don't understand why you would prefer a song that does not match your specialisation. Any ideas?
Iirc every girl has exactly one personal song, but not every of these songs matches the stat you are focusing on. What the guide is saying, is to save the song which matches your focus stat for last. Of course, if 2 or even all 3 songs match, you can use them earlier. But to be honest, it's not necessary to use these songs. Iirc the only advantage of using the special song is that you have a higher chance to get a break and such.
As for building up stats, iirc i did lessons on my primary stat until image level 10 or 11, then switched to my secondary stat until the image level is at least 14 on normal (since you need that to get an A ranking after the playthrough), and never did a lesson for the third stat, since i never used it anyway.