Yeah, I restrict them.
The exact set will depend on the campaign - my default is "anything from the PHB" or, if using a published setting "anything from the PHB or the setting book". That said, some settings feel better with more races - for something like Spelljammer I'll open the selection right up.
As regards player selection, my preference is that they either come to the table with a clear notion that they want to play a particular race, or if they don't have a strong preference then to default to human. I'm not keen on watching players spend a long time on that choice or, worse, deciding on which to use purely based on the ability score increases. (That said, that's very much a preference. It's more important to me that the player gets a character they're happy with than my notions about the "right" way to do anything.)