This is a tricky question
The Forgotten Realms are large. Very large. As a setting, it spans several D&D editions, many of which drastically changed the Forgotten Realms. Considering you're looking for information to (possibly) start playing D&D 5E, a lot of the older books may not be as useful to you. While they have a lot of information, they're not the most up to date versions of the story.
The Spellplague is a massive event that changed a lot of things in the Forgotten Realms, but you won't really find it mentioned if you look at books from earlier editions. In addition, you've not exactly narrowed it down a whole lot, you're essentially an alien asking another alien "so where do I start looking for more information on Earth?"
Like that alien's friend might, I'm going to suggest 'the human internet'. The Forgotten Realms wiki is most likely your best bet to start reading up on articles if you have a specific interest. Youtubers do a pretty good job at explaining the lore in bite-size chunks as well.
If you are looking for 5e-specific books, most of the official campaigns in the Forgotten Realms take place in a specific stretch called the Sword Coast, so if that's what you're interested in, the Sword Coast Adventurer's Guide has a lot of interesting information. Mordenkainen's Tome of Foes is another book that is very heavily lore-based, with information on the more extraplanar aspects of the Forgotten Realms, such as ancient races and other planes.
If you want to go back to the creator of the setting, you most likely can't go wrong with Ed Greenwood Presents Elminster's Forgotten Realms: A Dungeons & Dragons Supplement, which is a book written by the original creator of the Forgotten Realms, which wasn't made for any specific edition of D&D.
But like that alien in my example, you'll most likely first want to figure out what part of the Forgotten Realms you're specifically interested in.