Well, Falco tends to land more neutral hits in the neutral position, and be punished harder when he does get hit. Not like he didn't hit like a truck himself, but he is really, really fragile, so... :D
Common combo finishers would be: Bair, dairs sending them off the stage, fsmash/dsmash.
Bair is the reliable "I don't have any idea what to do anymore, let's just hit them offstage / out of position and work with that" (not that there's anything wrong with that, falco is good enough at edgeguarding to convert quite a few of those into kills... and positional advantage at lower percents is also quite fine)
Dair usually requires some planning on your part, or ****ty DI inputs from your opponent, but can be done (e.g. weak bair to carry them the last bit of the way and then dair, or a shine that sends them outwards when they are already close to the ledge).
Fsmash/dsmash are probably the most situational, but really fun if you can get them (some setups are shine under a platform, waveland on it, fsmash; dair/dash attack can combo into them at certain percents/DIs, and there is situations where many people miss techs if you put them in them. E.g. if you jump into them when they are already close to the ground, most people expect a dair and try to tech that. If you hit them with a weak bair, they'll land a few frames later and are probably techlocked from the dair-tech-attempt which obviously results in a free smash... or the infamous Sion-Combo consisting of stuff > uptilt > grab > fthrow > dair > dsmash)
Don't stress it though. If they do end up at high percents, don't try to force the kill (I tried that long enough, it just doesn't work against competent opponents
). Anything that will send them offstage is good enough at that point, and be it a nair/ftilt (bair is pretty good, but don't start doing nothing but them
).
And against floaties you can sometimes pick up surprise dtilts, which kill surprisingly early (rather underrated move).