Lol KO you don't question awesome xD - you just admire it with awe and wonder what you did in your past life to be so lucky to witness it.
Luigi
Luigi has some unique qualities about him. Let's take a look at them.
[Things to focus on]
Nair: This one's obvious. Luigi can do this quickly after taking damage, and for this serves as a great move to regain composure when being attacked as it's both high priority, and sends the opponent to a position they can't hope to continue their attacks from easily. There's good value in climbing with this attack as Luigi has more than enough jump in him to follow up.
Utilt: Off the bat it looks rather pathetic...I know, but this move is something that will get the ball started on combos. I suggest using this move in combination with Luigis wavedash, which as we all know is god-like.
Usmash: Like above works well while wavedashing. This smash hits a big area behind Luigi which has various upsides. Think of ways to use this to your advantage. *Cough out of shield.
Dthrow: Nice setup throw.
A, A, A combo: Although these are rarely used by most players in Melee, they aren't all bad. Granted I wouldn't suggest throwing them out as Mewtwo often. Luigis is fast to come out, and the third hit sends the opponent to a convenient place. Don't be shy to use the first two hits into a grab, dsmash, utilt etc.
Dsmash: A nice smash - use it xD.
Fair: CHOP! This can be used well at low altitude, and can be brought out twice like Marths in doing so. You can waveland this after a SH to follow it up, or use it while retreating backwards with a wd. Use while recovering to help cover the obvious flaw in this aspect of his game.
And lastly but not leastly,
Ftilt: Whats with this guy!? his ftilt is awesome...moreso than you'd ever think. Use it
[Things to avoid]
Dash attack: Wow...epic fail.
Using second jump early in recovery: His recovery sucks enough....don't do it.
'Normal' means of travel: Don't run around wd around. Only move normally if you're doing so walking.
Counting on fireballs: Use them sparingly as they're far from the ideal choice in projectile. That said they can be used well but it's at opportune moments they're worth their butter.
[Things to keep in mind]
Wavedash: = more movement freedom = advantage. Use wd with any and everything...grabs, tilts, smashes.
CC: With his traction this is a must. Can link into things like dsmash or dtilt well...though I wouldn't spam the latter.
Cyclone: Try using it to aid recovery. Every little bit helps. Be like Thunders!
IC's vs
Peach.
Wow what a doosey of a fight this is.
Okay, firstly keep in mind that Peach is very heavily an aerial character (albeit low altitude). When a character is in the air, it's safe to say you can go into your shield with very few exceptions (the only one with Peach is a Mr. Saturn really...which she won't have often).
Now that sounds good and well, but you need to keep in mind that Peach has herself a handly little abusive trick called Float Cancel. This pretty much means she will come out of air attacks and straight into grounded ones (very likely A, A slaps or dsmash) incredibly fast. You don't want her putting the pressure on you in this way or it's just a matter of time before you're minced :\. Get under Peach and land some upairs. You should be safe to do so for the most part. Doing this will hopefully deter her from dropping turnips on your head (or shiled) to whittle you away. WD is friend! Don't stay too far back from her at any time either, or the turnip lucky pluck will begin....which you don't want. Lastly shield grab and do what all IC mains do best - abuse the hell out of their dual-over mitt grab combos! Hope this helps.