Block Ciphers - Standardize plain text
You cannot encrypt 720 bits plaintext using just AES-128. AES is a 128 bit block cipher. Such a block cipher has an input of 128 bits of plaintext and an output of 128 bits ciphertext; and that's it. You need some kind of construction to make block ciphers encrypt larger or smaller plaintext.

Such constructions are known as (block cipher) modes of operation. Some of these constructs like ECB (usually insecure) or CBC require padding (what you call "expansion"), most of the others do not. Even ECB and CBC can be used with ciphertext-stealing to avoid padding.

Probably the best way is to chose a mode of operation that doesn't require padding; CTR mode operation is probably the most used mode for new implementations. It is also the most used within authenticated modes of operation such as GCM, which come highly recommended.

If you're stuck with ECB or CBC then choosing PKCS#7 compatible padding is probably the best / most compatible padding out there. Beware of padding oracle attacks though (did I mention authenticated encryption already?).