If you're simply trying to learn a gateway character (a character that you can use to get a feel for the mechanics before moving to a more complex character), try Marth. His moderately sized dash dances and wavedashes help you get a feel for the game's movement. His sword and grab helps you learn about spacing. Since his recovery is limited, naturally you'll teach yourself more about DI and varying your recovery options. While he's not the best character, he's best to learn the game through imo and is the most balanced when it comes to strength proportionate to tech skill.
Sheik isn't bad either. Her aerials and tilts help you learn about shield poking, gimping/edgeguarding, and spacing (without a disjointed hitbox like Marth's sword). Her grab game helps you get used to tech chasing. Her needles helps with camping, her up-b helps with learning how to vary your recovery options, etc. Since most of her aerials have little lag, quick, powerful, and link together easily, you may also get a feel of how to combo in this game. Some may disagree, but I think Sheik, out of all the characters in the cast, has the most moves that are actually effective with frequency in competitive play. Unlike Marth, she also has a sex kick, one of the most important moves in Smash. As many different characters have a sex kick in their pocket, learning to use Sheik's will serve you well later. Also unlike Marth, she has much better and more flexible Oos options that you can learn and get used to. On the flip side, you're more likely to learn the value of wavedashing and dashdancing through playing Marth rather than Sheik simply because he does it better. Plus, Marth's match ups are generally straightforward and easier to understand.
While Puff arguably utilizes the least amount of wavedashing out of the top tiers, she relies heavily on l-canceling and spacing. Depending on who you're playing, not knowing how to play Puff properly will get you slaughtered almost immediately due to her glass canon like qualities. She'll seem relatively straightforward and even an easy win character, but as you move higher and higher up the rankings, you'll find more and more players that know how to absolutely wreck any Puff aside from a few special ones.
Peach is decent for learning how to play defensive because she can utilize turnips, d-smash, floating, and various Oos options to promote that specific playstyle. She also requires very little wavedashing and other AT's, but her some of her moves can be laggy and very punishable/interruptable, which can make it difficult to get used to. She also arguably requires the least amount of L-cancelling, which practically makes "tech" skill per se very small at early levels. However, she still requires precision. In higher level play, missed moves can potentially lead to death if your facing a Fox or Falco.
Falcon is good for learning about SHFFLing and tech-chasing. Since Falcon has such an abysmal recovery, you may naturally learn how to play more safe and utilize baiting while still being on the offensive. Otherwise, he's difficult to use.
You can also play Fox and Falco on the side. Both of these characters are still excellent even without their shines. Their various recovery options using Up-b and side-b for example can help you learn different ways to recover back on stage. Falco especially can help you learn how to camp using lasers, which are possibly the best projectiles in the game. Since their so fast, playing and getting used to their speed will naturally get you used to the game's overall speed (for lack of better words). Plus, as Fox and Falco are among the most common characters you'll meet in tournaments, learning how they play will eventually benefit you in the end when learning different characters.
tl;dr or if you're not looking for a gateway character, just Marth and Sheik. Peach/Puff if you really don't want to learn how to wavedash.
Remember though that every character still utilizes wavedashing and wavelanding to different extents in the highest levels of play. It's very helpful to learn.
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