AES GCM mode encryption

GCM is an Authenticated Encryption mode. It provides you with confidentiality (encryption), integrity, and authentication (MAC) in one go.

So far, the normal modes of operation have been ECB (which is the default for Java), CBC, CTR, OFB, and a few others. They all provided encryption only. Confidentiality by itself is seldom useful without integrity though; one had to combine such classic modes with integrity checks in an ad-hoc way. Since cryptography is hard to get right, often such combinations were insecure, slower than necessary or even both.

Authenticated Encryption modes have been (fairly recently) created by cryptographers to solve that problem. GCM is one of the most successful: it has been selected by NIST, it efficient, it is is patent free, and it can carry Additional Authenticated Data (that is, data which stays in the clear, but for which you can verify authenticity). For a description of other modes see this excellent article of Matthew Green.

Coming to your concerns:

Padding: by default, Java uses PKCS#7 padding. That works, but it is often vulnerable to padding oracle attacks which are best defeated with a MAC. GCM embeds already a MAC (called GMAC).

Authentication: AES-GCM only takes one AES key as input, not passwords. It will tell you if the AES key is wrong or the payload has been tampered with, but such conditions are treated as one. Instead, you should consider using an appropriate Key Derivation Algorithm like PBKDF2 or bcrypt to derive the AES key from the password. I don't think it is always possible to tell if the password is incorrect or if the payload has been modified, because the data necessary to verify the former can always be corrupted. You can encrypt a small known string (with ECB AES), send it along, and use it to verify if the password is correct.

Minimise overhead: At the end of the day, all modes leads to the same overhead (around 10-20 bytes) if you want authentication. Unless you are working with very small payloads, this point can be ignored.

Performance: GCM is pretty good in that it is an online mode (no need to buffer the whole payload, so less memory), it is parallelizable, and it requires one AES operation and one Galois multiplication per plaintext block. Classic modes like ECB are faster (one AES operation per block only), but - again - you must also factor in the integrity logic, which may end up being slower than GMAC.

Having said that, one must be aware that GCM security relies on a good random number generation for creation of the IV.