If this is the first web design project you've done for money, here are a few tips.
1. Decide what your hourly rate is. Find out what other web designers are charging or what the acceptable rates are in your environment. Don't go too low or too high.
2. Work out how long the project will take to complete as best you can (be realistic). Then add 50% to that time.
3. Your lump sum for the project is your hourly rate multiplied by the number of hours.
4. Although clients prefer to be quoted a lump sum for the initial project so that they know what they are spending, this is not a good idea for post-launch work. This should always be done on a time rate basis.
In order to keep costs down, you need to take control of the project. Don't allow your client to have a daily input, this can be very disruptive and costly for you. Design a schedule of works that includes say, 3 design reviews at sketch design, comp/prototype and beta stages of the project. This gives your client the opportunity for input at key stages and keeps you free to work in between.
Of course, there's lots more but that should be enough to keep you going.