It really depends what question you're asking.
If you're asking what races 5e should get rid of from the published books... well, that's a moot question - they're not going to change the roster until 6e rolls around (or, I suppose, 5.5e - but I don't see that happening).
If you're asking what races I'd put in the 6e PHB (or, if I had a time machine, which ones I'd put in 'my' 5e PHB), my answer is "the same as the current PHB". I think the idea of including all those races that had appeared in a main PHB for any of the editions was a good one. (In fact, the big change I would make would be to add a couple of classes, to round out that roster in the same way - bring in an Assassin class, a Warlord class, and a Mageblade class to represent the BECMI Elf.)
If you're asking which ones I would include in a campaign, again it depends. When running a published setting, I'll typically allow the ones the setting recommends (so Eberron has the PHB races plus Warforged, Kalashtar, Shifters, and Changelings; Dark Sun has Muls and Half-giants but no Gnomes; and so on). When creating a campaign setting, I'll pick some set of races that seems good to me.
I usually encourage players to make their race selection really quickly: if they have a burning desire to play a member of a particular race, they should play that. But if they don't have a strong desire, they should default to human. Don't agonise over the decision!
I also tend to quietly discourage players from choosing 'oddball' races - that is, the ones that aren't in the PHB and aren't explicitly called out for the setting. However if a player does want to play such a race I'll almost always allow it, unless the setting lore specifically argues against it. (That is, if a player really wants to play a Tabaxi in FR, I'll allow it; but a player asking for a Drow in Dragonlance is going to be disappointed.)
Finally, I should note that I'm not particularly opposed to WotC publishing more races for 5e. However, I have no particular desire or interest to see any more (again, excepting the setting-specific races, which should be published alongside the rest of the setting). I'd much rather they published something else in the space.