The Realms is a tool, just like the material in the Momster Manual or the DMG.
In the Realms, the PCs are the most important thing for the DM to focus on--not the mountain of novels and sourcebooks filled with thousands of pages of Realmsore.
You'll get to that stuff, but you have a new campaign to run first. So do that.
You sound like an experienced DM, so find one or more low level adventures you've been dying to run, and plop them in the Realms. Let the PCs gain some levels while you all get familiar with the rules and what it's like to DM a new system (converting adventures to 5E ought to get you up to speed real quick).
Better to make mistakes early and often, before play progresses to mid and high levels.
Pick a place that's easy for DMs to start in, like Cormyr or the lands to the west. As play progresses, pick and choose elements of the setting that will spice things up, add flavor and that will interest your players (see Volo's Guide to Cormyr).
However you introduce these elements--especially NPCs--be consistent in your presentation every time. Don't overuse them. And find parts of the Realms that will challenge your players and give them a chance to leave their mark.
Remember: players like to tell stories about their characters.
Make the NPCs lively and memorable, keep your DM exposition short and to the point, and let the player's actions give you the opportunity to present more of the Realms.
For example: if you were using Myrmeen Lhal (the Lady Lord of Arabel--a major city in Cormyr), don't go on at length about her or how awesome she is. Instead, introduce her as the King's Lord, and let players figure out/learn who she is by interacting with her.
This puts you in the driver's seat and affords you the chance to run the NPC the way you see her, not the way the books present her.
And that's why you should run the Realms, because there are so many NPCs, dungeons, cities, towns and fantastic locations waiting for the DM to inhabit them.
It's like having an endless closet of really fine clothes that always Looks good on you, no matter what you choose to wear.
Good luck to you and good gaming, whatever choice you make.
