There are only 3 ways to generate unique values, rather they be passwords, user IDs, etc.:
- Use an effective GUID generator - these are long and cannot be shrunk. If you only use part or you FAIL.
- At least part of the number is sequentially generated off of a single sequence. You can add fluff or encoding to make it look less sequential. Advantage is they start short - disadvantage is they require a single source. The work around for the single source limitation is to have numbered sources, so you include the [source #] + [seq #] and then each source can generate its own sequence.
- Generate them via some other means and then check them against the single history of previously generated values.
Any other method is not guaranteed. Keep in mind, fundamentally you are generating a binary number (it is a computer), but then you can encode it in Hexadecimal, Decimal, Base64, or a word list. Pick an encoding that fits your usage. Usually for user entered data you want some variation of Base32 (which you hinted at).
Note about GUIDS: They gain their strength of uniqueness from their length and the method used to generate them. Anything less than 128-bits is not secure. Beyond random number generation there are characteristics that go into a GUID to make it more unique. Keep in mind they are only practically unique, not completely unique. It is possible, although practically impossible to have a duplicate.
Update: If you want 7 to 16 characters then you need to use either method 2 or 3.
Bottom line: Frankly there is no such think as completely unique. Even if you went with a sequential generator you would eventually run out of storage using all the atoms in the universe, thus looping back on yourself and repeating. Your only hope would be the heat death of the universe before reaching that point.
Even the best random number generator has a possibility of repeating equal to the total size of the random number you are generating. Take a quarter for example. It is a completely random bit generator, and its odds of repeating are 1 in 2.
So it all comes down to your threshold of uniqueness. You can have 100% uniqueness in 8 digits for 1,099,511,627,776 numbers by using a sequence and then base32 encoding it. Any other method that does not involve checking against a list of past numbers only has odds equal to n/1,099,511,627,776 (where n=number of previous numbers generated) of not being unique.