Authentication
The vast majority of the web will use RSA for the authentication key as it's widely supported but ECDSA is considerably faster (source). You can serve both RSA and ECDSA certificates for the best of both worlds (tutorial). Only support suites that are appropriate to your circumstances by checking for RSA and/or ECDSA in the authentication segment.
With RSA certificate:
TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256
TLS_ECDHE_RSA_WITH_AES_256_GCM_SHA384
With ECDSA certificate:
TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256
TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384