I would definitely recommend the Queen's Gambit, both Accepted and declined. Other than that, the Najdorf, Bogo-Indian and a few sharp lines of the Ruy Lopez are also great, not to leave out QID.
And there's another little-known opening with which I've had a lot of success; the King's Indian Defense, Sämisch, Bobotsov-Korchnoi-Petrosian Variation.
For the QGD you can look in to Marovic's book, or Saddler's book or Kasparov's Chessbase DVD, either of these is a very good introduction.
I'd say the French and KID share the similarities ThrillerFan mentioned but of course the pawn structures are very different.
The French (oddly) does have a little overlap with the QGD, as in the QGD you can get a reverse French advance structure after an ..Ne4 NxN dxe4. But it's not as large an overlap to trigger broad repertoire choices.
I prefer the QGD, which I play now, over the KID, which I played decades ago, because it's less theoretical and more of a let's play a classical opening and then let's play chess type of game. You need to pick a line to start with though, maybe start with the orthodox and then you see if e.g. you want to add something more dynamic like the Tartakower. The Tarrasch is also fine and better than it's reputation.
Great! Thank you for the advice and I will look into those resources!