Fundamentals are actually most important for a Falco to know
(i.e. timing, spacing and decision making), along with being able to get strong combos in general. Shine>dair (hit with the bottom of shine and then double jump>dair and remember to fast fall asap) can be good I guess but just to let you know, learning to convert smart lasers into big damage, learning to get decent to long juggles (as in 5-10+ hits, maybe all in one combo at low %), and learning to punish tech rolls will all do much more for you.
(If you're taking this game seriously)
When you shine>dair, assuming you did it onstage and the % was good so you're not getting punished for it (a floaty might punish that at low %), you now have to gamble in a tech chase or start relying on laser just to keep your offense going or start it back. When you juggle, your job becomes much easier. SHFFL Nair, D-tilt, Shine, F-air, Jab, Up Tilt, Up Smash and Up Air hit #2- Falco has all those options, you should study those moves and use them to juggle as hard/often as possible, and try to finish the combos with Fsmash or [shine>]Bair (roll the joystick in a quarter circle starting at the bottom and don't try to jump for B-air until you see you've turned around- so you don't get stuck in shine) when the other weaker moves will start sending too far.