Let me seperate up everything and solve approach each problem in isolation:
For authentication, baseauth has the advantage that it is a mature solution on the protocol level. This means a lot of “might crop up later” problems are already solved for you. For example, with BaseAuth, user agents know the password is a password so they don’t cache it.
Auth server load
If you dispense a token to the user instead of caching the authentication on your server, you are still doing the same thing: Caching authentication information. The only difference is that you are turning the responsibility for the caching to the user. This seems like unnecessary labor for the user with no gains, so I recommend to handle this transparently on your server as you suggested.
If can use an SSL connection, that’s all there is to it, the connection is secure*. To prevent accidental multiple execution, you can filter multiple urls or ask users to include a random component (“nonce”) in the URL.
url = username:firstname.lastname@example.org/api/call/nonce
If that is not possible, and the transmitted information is not secret, I recommend securing the request with a hash, as you suggested in the token approach. Since the hash provides the security, you could instruct your users to provide the hash as the baseauth password. For improved robustness, I recommend using a random string instead of the timestamp as a “nonce” to prevent replay attacks (two legit requests could be made during the same second). Instead of providing seperate “shared secret” and “api key” fields, you can simply use the api key as shared secret, and then use a salt that doesn’t change to prevent rainbow table attacks. The username field seems like a good place to put the nonce too, since it is part of the auth. So now you have a clean call like this:
nonce = generate_secure_password(length: 16);
one_time_key = nonce + '-' + sha1(nonce+salt+shared_key);
url = username:email@example.com/api/call
It is true that this is a bit laborious. This is because you aren’t using a protocol level solution (like SSL). So it might be a good idea to provide some kind of SDK to users so at least they don’t have to go through it themselves. If you need to do it this way, I find the security level appropriate (just-right-kill).
Secure secret storage
It depends who you are trying to thwart. If you are preventing people with access to the user’s phone from using your REST service in the user’s name, then it would be a good idea to find some kind of keyring API on the target OS and have the SDK (or the implementor) store the key there. If that’s not possible, you can at least make it a bit harder to get the secret by encrypting it, and storing the encrypted data and the encryption key in seperate places.
If you are trying to keep other software vendors from getting your API key to prevent the development of alternate clients, only the encrypt-and-store-seperately approach almost works. This is whitebox crypto, and to date, no one has come up with a truly secure solution to problems of this class. The least you can do is still issue a single key for each user so you can ban abused keys.
(*) EDIT: SSL connections should no longer be considered secure without taking additional steps to verify them.