Toise, there seems to be a pattern in each game where the character select screen is ordered to make nice looking rectangles, columns, or rows.
SSB
If we ignore all the four unlockable characters, we can see that there is a pattern based on the order the games the characters first appeared were released.
Mario, Donkey Kong - Donkey Kong (7/1981, Arcade)
Link - The Legend of Zelda (2/1986, NES)
Samus - Metroid (8/1986, NES)
Yoshi - Super Mario World (11/1990, SNES)
Kirby - Kirby's Dream Land (4/1992, GB)
Fox - Star Fox (2/1993, SNES)
Pikachu - Pokemon Red/Blue (2/1996, GB)
Now, we will look at the unlockable characters, we can see the same pattern occurring.
Luigi - Mario Bros. (9/1983, Arcade)
Captain Falcon - F-Zero (11/1990, SNES)
Ness - Mother 2 (8/1994, SNES)
Jigglypuff - Pokemon Red/Blue (2/1996, GB)
Melee
:random:
ichu:
:mewtwo:
:random:
The original pattern is gone but there seems to be a different pattern going on. First, we ignore all the six clones and the random slots.
First Row: Marioverse characters + SNES character
Second Row: SNES characters + Famicom character + GB character + Famicom Disk System characters
Third Row: Pokemon characters + GW character + Japan-only character (but they are all more popular in Japan than in North America)
The clones are added right next to the original characters, ignoring the aforementioned order.
Brawl
:random:
This is my favorite pattern of all with the SSB pattern coming in second place. Here, we can see that the pattern is based on defined groups occurring in columns. And best of all? The unlockable characters now can be counted with the starting characters in this pattern!
Column 1 - main characters from the Mario main series
Column 2 - main characters from the Mario spin-off franchises
Together, columns 1 and 2 consist of Marioverse characters.
Column 3 - main characters from the Zelda series
Column 4 - main characters from Famicom Disk System and Famicom
Notice how Link is right next to Samus. The original Zelda game was a Famicom Disk System game so it makes sense for Link to be right next to Samus and followed by the other NES-era characters.
Column 5 - main characters from Kirby series plus Olimar
Column 6 - main characters from Star Fox series plus Captain Falcon
Notice how both Kirby and Star Fox each have three characters with both captains at the bottom. Also, Olimar seems to be a cutesy character like the Kirby characters so it might make sense for him to be grouped with Kirby characters. Star Fox and F-Zero were originally SNES games so it would make sense for Captain Falcon to be grouped with Star Fox characters. Olimar and Captain Falcon are both captains and they are right next to each other.
Column 7 - Pokemon characters
Column 8 - Fire Emblem characters and Mother characters
Pokemon, Fire Emblem, and Mother are all RPG games so together, both columns 7 and 8 have RPG characters and they tend to be more popular in Japan than in North America.
Column 9 - Mr. Game & Watch plus the third-party characters
This column is essentially the WTF column because Mr. Game & Watch was originally the WTF character in Melee and both Snake and Sonic are not Nintendo characters so it kinda make them seem out of place.
You see, Toise, there is a reason why some of us think that there might be a pattern on the character select screen in SSB4. For all we know, it could be something like this.
:random:
Row 1: Marioverse characters plus Mr. Game & Watch but it makes sense because of his history with the Marioverse characters in Game & Watch Gallery games.
Row 2: NES-era characters. Snake is from this era, too.
Row 3: SNES-era characters. Sonic is from this era, too. Olimar is the only one out of place but there is really no other place he could go on the roster.
Row 4: RPG characters
Also, notice the first column. We got Mario, Link, Kirby, and Pikachu. The first four characters announced for Brawl. And the last column got third-party characters.