I recommend you check out books like the Elemental Evil Player’s Companion and Volo’s Guide to Monsters to really broaden out your selection of playable races. Those races are awesome and they add a lot of fun and flavor to D&D, but we’re already looking at nine options just in the Handbook.
It leaves out my favorites, too - no Aasimar, no Warforged, no Goliaths or Genasi. This is an overview of the racial options in the 5th Edition Player’s Handbook and yes, this leaves out some of your favorites. Things we will not be doing include going over the history of each class, so there won’t be yet another paragraph of me going originally, Elves and Dwarves and Halflings were classes you could play, not races at all because we’ve all heard Grandpa Rossi sit in his rocking chair and go on and on about the old days of box sets and hex maps. If you remember our Dungeons and Dragons Classes 101 roundup, we’re using the same format here for our overview of the various races one can play.