Lunalu in Rising is the gold standard for random select characters.

[FGCNN | Nurdell]

If you were afraid to play random select characters in the past like Mokujin or Eleven - Lunalu comes to save the day. This little artisan will draw you a character, the drawing wil come to life. And if she really likes her work (namely handsome men) her eyes will sparkle.

Press R2 in character select screen, and you'll see a tick list on what characters you want to be randomized into, and which to exclude.
There's also an option on top to randomize the character for each match, or keep the same.

So yeah. Great features. I love random select chars, and unless somebody would point out a game with the selection list too; I will say - Lunalu is the best there was.
And it might be slightly harder to host full random tournaments in the future, I guess. Haha.

[KensouADV]

Both DOA5 and DOA6 have this with both characters and stages.
Yeah, it's pretty nice to have. Wish Bamco recent games didn't ditch Mokujin/Edgemaster characters.
Just wish I could buy individual characters in the f2p version. Already own the previous game and not into buying this one before a sale but I would get my main if I could.

[Pacho]

As someone who plays random select, Lunalu was a godsend for me.

[Isaiah]

If anyone is afraid of Mokujin that's funny to me.