Make my website contact form and newsletter email subscription work.

I have built my own website off a free template that uses Html5, CSS3 and js. I need the contact form to work - send the information that a customer may type into the form to my email address. My form consists of: Name; Telephone number; Email; and Content. Also, on the footer section on all the pages on my website, there is a single "form" where customers can enter their email address and subscribe to receive email updates. I need those email addresses to go into some form of database that I can use. I am not 100% how this usually works but I understand that the contact form need a PHP script to work in conjunction with the Html on the contacts page.
I also need the form to make sure that the correct information is being typed in. i.e. - numbers into the phone number section and that an email is typed in the email section. And I'm guessing it would be a good idea to have a captcha on my contact page?

My web host/ server that I use has provisions for mySQL as well as use the latest PHP script.

I also need a favicon to work with/ on all my page tabs. I can't seem to get it to work.

I am looking for a once off quote on the above job and NOT a per hour quote. Please also let me know what you will all need from me.