Securing a UDP connection

For a personal MMO game project I am implementing a homebrew reliable UDP-based protocol in java. Given my current setup I beleive it would be relatively simple for a snooper to hijack a session, so in order to prevent this I am taking the opportunity to learn a little cryptology. Its very interesting.

I can successfully create a shared secret key between the client and server using a Diffie-Hellman key exchange (a very clever concept), but now I need to use this to guarantee the authenticity of the packets. My preliminary testing so far has shown that the couple of different ciphers Ive tried bloat the amount of data a bit, but I would like to keep things as small and fast as possible.

Given that I am only trying to authenticate the packet and not nessecarily conceal the entire payload, I have the idea that I could put an 8 byte session ID generated from the secret key into the packet header, encrypt the whole packet, and hash it back down to 8 bytes. I take the unencrypted packet and put the 8 byte hash into the place of the session ID and then send it off.

Would this be secure? It feels a little inelegant to encrypt the whole packet only to send it unencrypted - is there a better/faster way to achieve my goal? Please note I would like to do this myself since its good experience so Im not so interested in 3rd party libraries or other protocol options.

If both peers have access to a shared secret (which they should, since you're talking about Diffie-Helman), you could simply store a hash of the datagram in its header. The receiver checks to see if it matches.

As an added security measure, you could also add a "challenge" field to your datagram and use it somewhere in the hashing process to prevent replays.

So this hash should cover:

The shared secret
A challenge
The contents of the datagram

EDIT

The "challenge" is a strictly incrementing number. You add it to your datagram simply to change the hash every time you send a new message. If someone intercepts a message, it cannot resend it: the receiver makes sure it doesn't accept it.