Which asymmetric cipher provides the highest performance? To get the highest performance, which asymmetric cipher provides the fastest encryption/decryption? ECC or DH? What key size is recommended today?
I prefer a ~128 bit security level. With ECC this means a curve with ~256 bits, with DH or RSA this corresponds to around 3000 bits. If you can accept a lower security level, the advantage of ECC over DH/RSA gets smaller.

My favourite is Curve25519, which has easily available high performance implementations. An alternative is P256 which is a NIST standard, but a bit slower. There are also some other curves/implementations which are faster than Curve25519, but those seem more academic.