My tier list!
My tier list is divided into viable, semi-viable, and not viable, but since i don't know enough about the semi-viables and lower to rank them, i've just ranked the viable characters
1: Falco/Fox
2: Sheik, Marth
3: Jigglypuff
4: Peach, Ice Climbers
5: Falcon, Dr.Mario
1: I believe falco does better on average in most mus, but I have him tied with fox because fox does significantly better vs puff and peach. The significant attribute of this tier is that these characters have no BAD mus (40-60 or worse)
2: What's most important about these characters is that they can compete with tier 1, having evenish mus with both fox and falco. I think sheik does a little better than marth vs falco and a little worse than marth vs fox. Sheik also has the benefit of destroying the low tiers and having very solid mus vs the mid tiers. She also beats marth in the head to head. However, sheik does lose to ICs and puff pretty solidly.
Marth has the benefit of having FD vs fox and falco in the current ruleset Best of 5s, which sways the mus to his favor for that one (possibly 2) game(s). He struggles much more vs mid tiers such as pikachu (if u type pikachu it wants to correct it to spinach), but likely wins those mus regardless, so this isn't weighed that heavily.
The difference between these two isn't that big, which is why they are in the same tier, but since marth loses the head to head solidly I rate Sheik slightly higher.
3: Jigglypuff would easily be in tier 2 if it wasn't for her bad mu with fox. She slightly beats falco, beats sheik, and is evenish with marth, possibly beating him, but her mu with fox is BAD. I weigh this very heavily since he is in tier 1. She also struggles much more with mid tiers (and some low tiers) than tiers 1 and 2 (the fact that people are even discussing whether she is even with ylink shows this).
4: Peach gets a lot of points just for being evenish (55-45) vs falco, since the rest of the characters don't really have this ability, and again this is weighted heavily because he is tier 1. She does lose badly to fox, but not much or any worse than the rest of this tier (they all for sure lose to fox). She is actually pretty weak besides falco, since she loses to sheik, is evenish vs marth, and loses BAD to jigglypuff. Peach vs ICs however is probably the worst mu of all the possible mus in the viable tier (in peach's favor).
ICs can be argued to be better than peach since they have a much better mu vs sheik and jigglypuff. They lose to tier 1 for sure, especially fox, but they have a lot of tools to deal with falco... I will be honest and admit that its hard for me to rate ICs since i don't believe i solidly understand them as a character and am not sure how their mus vs tier 1 really go. Their main downside would be having a somewhat hard counter in peach. This rating is assuming wobbling is legal. I guess id have to rate them slightly lower since they lose so badly to peach.
5: I actually think Falcon is pretty bad because he plays so straightforward. I just see him solidly losing to falco and fox, with not much room to gimmick them. Dr.Mario has very similiar mu ratios to falcon vs fox and falco, but i think his moveset and playstyle is conducive to stealing wins more often. They both lose to sheik solidly, both evenish with marth (id say falcon is better though), same thing goes for jiggs (but id say doc is better), then falcon does better, beating peach and ICs. Head to head is evenish.