Short summary: Don't do it, use an established password hash function like bcrypt, scrypt or PBKDF2.
Long form:
What you are doing here in effect is this:
- Create a combined hash algorithm out of several different hash algorithms (or block ciphers made into hash functions).
- Use a salt input to the combined algorithm to decide which of these algorithms to call in which order.
- Store the salt and the resulting hash.
There are three ideas hidden here: A salt, repeated hashing, and use of different hash functions.
The reason to use a salt for password storage (or any usage of a password, really) is to avoid that the attacker can simply use a rainbow table - or, in fact, to make the needed rainbow table that many times bigger. As an example, if you have tree algorithms which will all be used, in a random order, you in effect have 6 possibilities (123, 132, 213, 231, 312, 321), which means a rainbow table has to be six times bigger.
At the same time, the hash execution time will be three times longer, so generating the rainbow table takes in effect 18 times the original time.
To make a rainbow table attack totally ineffective, you use a salt that big that it is not practical anymore to use a rainbow table (since it would need to long to generate and too much space to store). The Bcrypt algorithm, for example, takes an 128 bit salt input. A rainbow table for just a single password and all possible salts would take $2^{128}$ entries.
A salt alone still does not help against a brute force attack - you can check all realistic passwords in a dictionary for MD5(salt | password) == hash
just as fast as MD5(password) == hash
.
Here your second idea comes in: Repeated hashing. In your example, you use three hash invocations for each password - this means brute-forcing a single password takes three times the time as brute-forcing it with a single hash function. Three times is not much.
Instead, use a lot larger number of hashes. There are specialized slow hash functions around (like bcrypt), which have a configurable work factor build in - e.g. they take beside the hash and password input a work factor parameter, which says how often is should loop. You then can simply scale this with the hardware progress so your user does not have to wait too long for login, but an attacker still needs very long to crack the password.
Other schemes (like PBKDF2) use a fast hash function (like MD5, SHA-1, SHA-2) a large number of times (something like Hash(password, hash(password, hash(password, ...(password, hash(password, salt))...)))
).
Your third idea is using a different hash algorithm depending on the salt.
Using a different salt as input to a hash function has a similar effect to using a different hash function, but is much simpler to implement. Using different algorithms makes your combined algorithm harder to analyze (i.e. harder to guess about its security), and also harder to implement. Also, you are depending on the security of multiple algorithms.
I could think about using different algorithms to secure against cryptanalytic breakthroughs in any of them, but then you should always use all of them, and there is no reason to randomize which algorithm to use.
So, don't do this, use instead an established password hash function like bcrypt, scrypt or PBKDF with an appropriate work factor. (These all include the use of salt.)