Please read this article in its entirety, and feel free to come back to post further comments or new questions.
Cryptographic Right Answers
In particular, the very first question answered is:
Encrypting data: Use AES in CTR (Counter) mode, and append an HMAC.
AES is about as standard as you can get, and has done a good job of
resisting cryptologic attacks over the past decade. Using CTR mode
avoids the weakness of ECB mode, the complex (and bug-prone) process
of padding and unpadding of partial blocks (or ciphertext stealing),
and vastly reduces the risk of side channel attacks thanks to the fact
that the data being input to AES is not sensitive. However, because
CTR mode is malleable, you should always add an HMAC to confirm that
the encrypted data has not been tampered with.
And the very next question answered is:
AES key length: Use 256-bit AES keys.
Theoretically speaking, 128-bit AES keys should be enough for the
forseeable future; but for most applications the increased cost of
using 256-bit keys instead of 128-bit keys is insignificant, and the
increased key length provides a margin of security in case a side
channel attack leaks some but not all of the key bits.
[EDIT 1] Also, the fact that you've applied a "public-key-encryption" tag to your question implies that your understanding of cryptography could be better. Please also read chapter 5 of Security Engineering (PDF) by Ross Anderson; it's free and very accessible.