Yes, RSA and AES are two very different things:
- RSA is public key cryptography, involving a public key and a private key, and is fairly slow. The primary use is to set up a secure exchange of a symmetric encryption session key.
- AES is symmetric encryption, which is fast and secure.
Since your app does not communicate over public channels and the use of cryptography is limited to product activation/registration you'll want to go with a symmetric cipher. The benefits of public key ciphers is in key management, which you will be handling on your web site or through email.
Note that you do not have to distribute the same key for every customer. You could generate a hash of some of the registration info and XOR it with something else (a fixed session key, perhaps). Send that to the customer, and the program could generate the same hash and XOR will the key you sent to produce the original fixed key.
Dealing with cryptography is not something to be done lightly. As you mention, you expect this to be cracked. If you're doing your own this will almost certainly happen. You can still use your own implementation to "keep honest people honest," but realize that's as far as you'll get. If you need something stronger then you should purchase a solution after doing thorough research on the solutions.