I'd like to know how safe the TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA Cipher (Cipher ID: [0xc009]) is. Alternatively, I'd appreciate to be directed to some sort of list that lists all available Cipher Suites from strongest to weakest.
It is safe, but not ideal. Let's break it up into its individual components:
ECDHE - This is the key exchange mechanism. It is diffie-hellman key exchange using an elliptic curve, typically a NIST curve such as P-256. It provides forward secrecy, because each key exchange uses a different, randomly generated private key.
ECDSA - This is the algorithm used to sign the certificate. Like DSA, each signature requires high-quality random numbers. The failure of the RNG during even one signature can reveal the private key. This makes it rather fragile, but when used correctly, it is secure. The alternative is RSA which is the industry standard, but uses bulkier keys and signatures.
AES_128 - The symmetric cipher is 128-bit AES, a secure block cipher and the NIST standard. Virtually all TLS connections use AES. Most key exchange algorithms do not provide much more than 128 bits of security anyway, so there is little reason to use a larger key size.
CBC - Block ciphers require a mode of operation, and CBC is one of them. While it is fine in theory, it is notoriously easy to get wrong and has been the source of numerous padding vulnerabilities in the past. Any modern version of TLS should not be vulnerable to these, even with CBC. CBC is an unauthenticated mode, which brings us to...
SHA - An HMAC, a type of keyed hash, is used to provide integrity. It is given a secret key which allows each side of the connection to verify that the data has not been tampered with in transit. In this cipher suite, SHA-1 is the algorithm used with HMAC. While SHA-1 has been found vulnerable to a collision attack, that is not relevant for its use in HMAC.
Rather than just using this one cipher suite, why not follow best practices?