ECIES is not present in the normal Java libraries, at least not up to the current date. You have to use a library like Bouncy Castle.
For quality of the curves you could take a look at http://safecurves.cr.yp.to (if you have the stomach for it). Each set of domain parameters is always directly tied to the key size. I like Brainpool curves myself; they are relatively standard and relatively safe if you use them with some care.
Note: never directly encrypt plaintext with RSA, DSA or ECIES, always try and use hybrid cryptography. So compare with input sizes of 128, 192 or 256 bits at most.
So, without further ado.
public static void main(String[] args) throws Exception {
Security.addProvider(new BouncyCastleProvider());
KeyPairGenerator kpg = KeyPairGenerator.getInstance("ECIES");
ECGenParameterSpec brainpoolP256R1 = new ECGenParameterSpec(
"brainpoolP256R1");
kpg.initialize(brainpoolP256R1);
KeyPair kp = kpg.generateKeyPair();
Cipher c = Cipher.getInstance("ECIES");
c.init(Cipher.ENCRYPT_MODE, kp.getPublic());
final byte[] aesKeyData = new byte[16];
SecureRandom rng = new SecureRandom();
rng.nextBytes(aesKeyData);
byte[] wrappedKey = c.doFinal(aesKeyData);
SecretKey aesKey = new SecretKeySpec(aesKeyData, "AES");
Arrays.fill(aesKeyData, (byte) 0);
}