Whatever you're most comfortable with provided its not something like the Englund Gambit or Albin Countergambit. There are bad responses like I just mentioned but theres no "Best Response to 1.d4"
Are you looking for counterplay?
Then try 1...Nf6 and go for a King's Indian Defense main line with 6...e5 and then either 7...Na6 or 7...Nc6. KID is quite theoretical though, just warning you. And you will also need to know more than just the Classical variation such as Saemish, 4 Pawns Attack, Fianchetto Variation.
Or play 1...Nf6 and go for the Nimzo Indian or Bogo/Queens Indian. They offer counterplay for Black (although potentially less than KID) but more solid than the KID.
Are you going to look for super aggressive counterplay?
Then try 1...f5 the Dutch Defense which has 3 Branches: the Stonewall, Classical, and Leningrad. You will need to know 1 of these + anti-Dutch lines unless you start with the 1...e6 move order (which only applies for the first 2 branches). The Dutch can also be played vs. other openings like 1.c4 and 1. Nf3.
Or perhaps just a solid game?
Then play 1...d5 and go for the solid QGD! Or play 1...d5 and go for the Slav Proper with 4...dxc4. The Slav Proper can get more sharp than the QGD though, but its still solid. Some people say the Semi-Slav is quite solid but they couldn't be more wrong especially when it comes to the Botvinnik or Anti-Moscow Gambit variations which are ultra sharp and theory loaded.
Or just a somewhat more open game?
Then play 1...d5 and go for the QGA. It is quite sound but you will have to know how to defend IQP positions where white has an IQP at d4.
what is the best Response to 1.d4?
Is it 1.d5,1.Nf6,1.g6,1.c5 or else?
Leave your answers in comments