Good discussion point. I'll lay out a few of my thoughts on focusing on certain aspects to improve.
Tech Skill
Obviously this is huge. If you can't do what you want, you basically can't even play the game. Someone who can't WD isn't playing the same game as someone who can, and are going to struggle as a result. Even someone who can WD but has to focus on it is at a severe disadvantage compared to someone who can do it automatically, without hesitation. People hear it all the time, but tech skill really is all about proper practice. I spammed buttons for years to warm up, but these days I have a disciplined warm up routine that I do no matter what. It sucks to go to a tournament and when I finally get there I have to sit and do a routine instead of start playing right away, but it definitely pays off. There's tons of different ways to practice tech, but ultimately you should be doing something along the lines of picking a single technique, performing only that tech 10, 20, 50, even 100 times depending on how much you're struggling with it, and also FOCUS. You need to force yourself to hone in on each individual animation, each frame. If you don't do that, your mind and body will not calibrate your muscle memory properly and the sloppiness will come out, if not during friendlies, then during tournament.
Neutral Game
There's a lot of optimization to focus on in Melee, but I think ultimately players should become comfortable in neutral once they have their tech down. I think it's the most abstract aspect of the game, so the earlier you start focusing on it, the better. What constitutes neutral is obviously a gray area, but essentially it boils down to things like stage control, footsies, spacing, baiting, mixups/RPS, adapting, conditioning, and so much more. While you may not get a ton of wins focusing on neutral at low level, especially as Falco who relies on his punish game way more than a character like Samus who usually tries to win neutral over and over, you will develop fundamentals that make it easier to improve in other aspects. It's way easier to practice your punish game when you're able to win neutral 9/10 times.
Punish Game
Once you feel competent in a certain neutral scenario, you can start to focus on punishing. Let's say you are consistently cornering your opponent or keep landing shinegrabs, but in both of these scenarios you don't get much, if any, percent. You can look at what hits you are getting and either work on improving your punish off of those hits, or readjust your neutral so that you can land an initial hit more conducive to comboing. Maybe you can win neutral spamming AC bair or reckless FH aerial through an opponent on a plat, but if you can't get a followup then maybe you're not really "winning" neutral after all. Overall, improving your punish game is difficult, but still relatively straightforward. You want to maximize your opportunities with damage, but also balance that with the next section.
Edgeguarding
Way too many people lose sets because they don't get the key edgeguards. Back in the day people always staged on stage and just attacked people as they tried to sweetspot and did their best to prevent them from getting off the ledge if they grabbed it. Today's meta is drastically different and an indirect result of the differences seems to be blurring the line between punishes and edgeguards. Players have to proactively cover multiple options instead of relying on simple RPS guessing, and closing out edgeguards means so much more in a meta where the ledge offers many options with actionable invul and punish games are harder in general. It doesn't matter if you can get someone to 100% and knock them off stage if they're going to recover, rack up the same damage on you, and then actually get the KO. If you have matches recorded or even just have a friend who can watch you play, keep track of how many edgeguards you capitalize on. If you're not sure what constitutes a recovery, I'd just say situation where the opponent has to up-B or airdodge to make it on stage or situations where the opponent goes into the side blastzone magnifier (though you can certainly include any off stage scenarios if opponents are frequently DJing to the ledge for free).
Matchup Knowledge/Style
Matchups are all about fine tuning your game to work around a certain character's attributes. There's so much to talk about when it comes to matchups, and I think it's harder to discuss than people think because of how differently everyone plays. While there is tons of value in learning how other Falcos approach a matchup, you have to be open to the idea that your own personal play might be styled differently. Take as much as you can from other players and learn how you can fit that with your own style. By style, I don't mean a bunch of tricks or habits you do all the time. I mean your mental game and the things you are naturally best at. If you look at Westballz, he's a combo monster, and he's developed his play around that. He plays in a way that forces the opponent to have a better punish game than him then beats them because they don't. That doesn't mean he doesn't do other stuff effectively like win neutral or adapt, but his punish will always be his bread and butter, the aspect of his game he can rely on when nothing else seems to be working. For PP, I'd say he relies on his neutral with laser and DD control more than anything. These are very generalized views of their styles, and you could go WAY more in depth about what makes Wes's punishes or PP's neutral so good, but ultimately you need to figure out what your strengths and weaknesses are so you can downplay your weaknesses and exaggerate the effect of your strengths. Once you do this, your approach to a matchup becomes more obvious, and it's way easier to take aspects of gameplay from other players and sort of plug them into your own gameplay.