Hmm... I'll take a shot at this! Here's my own thought process, though - I want to have a focus on characters that have affected the world of gaming enough to warrant their inclusion in Smash Bros. proper, whilst still practically being fourth-party. However, I'm not fussed with things like "oh they have to be connected to Nintendo", as long as it's logical to see them. Starting out:
Challenger Pack One: Mametchi Was Raised For This!
Thoughts: Okay, Tamagotchi might seem like an odd choice given the amount of crossover between the series and video games, but technically speaking, digital pets aren't considered "video games" despite being similar. Notably, the series was created by Bandai (the toy one), but obviously they've come into the fold of Bandai-Namco these days - and there's even history with Nintendo considering the Mario Kart Arcade GP sub-series! Notably, Mametchi is considered "the main character" of the series, hence his inclusion! In terms of moveset, I'd want Mametchi to be fairly simple to understand with lots of references to various parts of his series - he'd be pretty light and floaty, but overall mechanically simple and inviting for newcomers.
Challenger Pack Two: Tony Hawk Ollies into the Arena!
Thoughts: With a high-octane moveset focusing on a highly mobile rushdown archetype that doesn't handle being hit very well (after all, being knocked off a skateboard isn't something you can instantly recover from), Tony Hawk would bring a lot of mechanics and ideas seen from not only the Tony Hawk's Pro Skater series, but from extreme sports as a whole - though, of course, with a major focus on skateboarding. The Pro Skater series is a pretty important one in gaming history, too - being one of a line of system-sellers for the PS1, and a series that's existed (for better or worse) as a constant force in the gaming world since then.
Challenger Pack Three: Turok Hunts Down A Victory!
Thoughts: The Turok series is interesting in that, these days, it's more thought of in terms of video games than in terms of the Valiant Comics series that they actually spawned from. In terms of his design and playstyle, it would mostly be focused on his N64 outings in the first-person shooter genre, though Turok also has access to a knife and overall has a moveset focused on rapidly overpowering and subduing enemies, in keeping with his nature as a hunter - a dinosaur hunter, you might say. I also think it would be cool for him to have a mechanic similar to Witch Time utilising the Chronoscepter.
Challenger Pack Four: Pepper Roni Delivers a Win!
Thoughts: I knew that I wanted a LEGO character to make it into the roster, given a long history of LEGO games - both original titles like LEGO Creator, Bionicle, and LEGO Worlds, and LEGO-themed licensed works like Harry Potter, Marvel Super Heroes and Star Wars. Whilst you may scream something along the lines of "TONY HAWK ALREADY HAS A SKATEBOARD", my thought process here is that Pepper's moveset focuses a lot more on the LEGO side of his nature - that is, creativity. I'd also like to have some little hints and references to other LEGO IPs here and there too - the neutral air being a reference to Ninjago's Spinjitzu wouldn't be a bad shout.
Challenger Pack Five: Yugi Gets Ready To D-D-Duel!
Thoughts: Yu-Gi-Oh is in an interesting situation in that, technically, it is a game - though being card-based, despite the license apparently being owned by Konami. Overall, Yugi's character archetype is primarily focused on that of a "summoner" - utilising the various monsters and beings from within the cards to battle on his behalf. However, Yugi also has the ability to utilise dark magic - given that he's going to be in his Pharaoh form here - which allows him to still fight whilst using the various summoned beings for a combination of stage control and pressure, as well as potentially powerful trapping tools. Yu-Gi-Oh has been popular almost ever since it's been in existence - and I think Yugi would be an interesting inclusion into a game like this.
Challenger Pack Six: Geralt of Rivia Slays the Competition!
Thoughts: The Witcher series is a pretty interesting one to look into, given its connection to Slavic mythology - and its origin as a book - not to mention that The Witcher 3: Wild Hunt has the dubious honour of having one of the largest development teams of all time, as well as the less dubious honour of being near-universally praised. Overall, whilst he might seem like "another swordsman", I think Geralt could bring a unique moveset that could make him feel, at least conceptually, like a "heavier Link" - though with more magical elements and a degree of interplay between his different swords, perhaps. I don't know as much about this series, but I know it's important!
I think this is a good place to end off on. Each of these characters, in some way or another, has impacted gaming, but also culture - be it through the meteoric rise of virtual pets in the late 90s and early 00s, the ever-presence of trading cards in the collective consciousness, the interesting history of open-world games and PC gaming, a look into the culture and history of places we don't usually see, a world-class reinvention of an entire gaming genre, or a game that essentially kicked off a genre of its own - a group of characters important enough to gaming to warrant inclusion in Smash, despite being fourth-party.