How do I make a web server to make timed multiple choice tests?
When the server-side creates the form, encode an hidden field with the timestamp of the request, so when the users POSTs his form, you can see the time difference.
How to implement that is up to you, which server you have available, and several other factors.
I'd like to make a webapp that asks people multiple choice questions, and times how long they take to answer. 
I'd like those who want to, to be able to make accounts, and to store the data for how well they've done and how their performance is increasing.
I've never written any sort of web app before, although I'm a good programmer and understand how http works. 
I'm assuming (without evidence) that it's better to use a 'framework' than to hack something together from scratch, and I'd appreciate advice on which framework people think would be most appropriate.
I hope that it will prove popular, but would rather get something working than spend time at the start worrying about scaling. Is this sane?
And I'd like to be able to develop and test this on my own machine, and then deploy it to a virtual server or some other hosting solution. 
I'd prefer to use a language like Clojure or Lisp or Haskell, but if the advantages of using, say, Python or Ruby would outweigh the fact that I'd enjoy it more in a more maths-y language, then I like both of those too.
I probably draw the line at perl, but if perl or even something like Java or C have compelling advantages then I'm quite happy with them too. They just don't seem appropriate for this sort of thing.