I need to hash a message into a string of 30 chars. What's the best and most secure hash function for this usage?
Thirty characters (bytes) is 240 bits.
If you can't move the goal-post to allow 32 characters, then you will probably end up using SHA-1, which generates 160-bits or 20 bytes. When Base-64 encoded, that will be 28 characters. If you use a hex-encoding, it will be 40 characters, which is nominally out of range. With 32 characters, you could use SHA-256, but Base-64 encoding would increase that size (to 44 characters) and hex-encoding increases the size to 64 characters.
If you must use hex-encoding and can go to 32 bytes, then MD5 - which generates 128 bits - could be used, though it is not recommended for any new systems. With Base-64 encoding, MD5 uses 24 characters. Otherwise, you are using very minimally secure algorithms - not recommended at all.