Lets get real here; it should just be Human Bard.
First off, I wouldn't use 5e as the chassis for even this much of the discussion; 5e's classes are so watered down that each would need a full redesign to fit into this framework.The book will have 5 races/species/whatever and 5 classes. And before anyone says anything yes I am aware that in old Basic there as just classes as Elf was a class and Dwarf was a class etc, but just go with me on this.
Out of the whole of 5E D&D what would you like to see as the Basic Core Races and Classes?
Let's also apply ONE subclass to represent the whole class. So not just Ranger but Beast Master Ranger as the one and only Ranger in Basic (and possibly filling the only frontline melee slot).
So, 5 classes with 1 attached subclass each and 4 races as we can assume Human is a default choice.
You guys are thinking to much about what boils down to a "pick your top 5 races and classes" list.
In fairness, my "top 5 races and classes" is very different than, "What would you recommend in terms of classes and/or races for a streamlined version of 5e, akin to Moldvay's Basic?"
My top five classes:
Monk
Warlock
Fighter
Rogue
Anything but Bard
My top five races:
Human
Variant Human
Human, but something happened (Reborn, etc.).
Human, but in a different, more human-y way.
Anything but a soulless, dead-eyed elf.
No more humans, please.Lets get real here; it should just be Human Bard.
Uh.. I did. And they asked what would be in a Basic game that "trims things to the bone". That's not "What are your top 5 species and classes?", that's asking what I think the basic species and classes would be. To which the answer "the ones that were already published in the 5E Basic Rules" applies.You could just read the post.
Ok, I'll answer what I think the question is, based on the original post and then this response. I'm reading it as "What would be a good, shrunk down list for a new Basic D&D assuming modern-day preferences?"You guys are thinking to much about what boils down to a "pick your top 5 races and classes" list.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.