Hello empyrean,
To be honest, three weeks means you're in for a very steep learning curve. Somewhat frightening. I would strongly recommend you either try to get a budget for commissioning some of the work or ask for more time.
That said, my recommendation would be for PHP and MySQL. You can read and learn about PHP from www.php.net and hosting for the two abound; there are even free hosting packages to get you started.
What you're asking isn't too complicated per say BUT from my experience people that commission projects will always want more bells and whistles built in. Do you have a written specification for the design and functionality of the site?
I hope that gets things rolling for you; come back to us when you need more information.
And good luck!
Regards,
David