SSL uses several encrypt algorithmic at different points.
Typically it will use a asymmetric cryptography authenticate the hosts and establish trust between the client and server. Then a random key will be generated and shared between the hosts and a symmetric cryptography algorthim will be used for the actual payload.
Typically the asymmetric key will be RSA with key sizes of 1024, 2048, or 4096. The key size doesn't really affect the symmetric that is used for the payload. These days most certificate vendors will sign a 2048 or 4096 certificate request, key sizes of 1024 are pretty weak. While most CA keys are 2048 bits, many will sign larger keys, so you don't have to limit your private key to 2048 bits.
The symmetric algorithim that is used will depend on the client and server. The client and server will select the most secure option available. If you are using apache then you use the
SSLCipherSuite to select which symmetric ciphers you will permit.
Asymmetric cryptography is has the large sizes of the keys(2048,4096), and it is very slow. That is why it is only used during the initial phase. Once the connection is established, communication happens over the relatively fast symmetric cryptography which uses the smaller key sizes (128,256).