If you plan to make a living out of it charge per project according to work, investment and other factors you think are important to you.
To give you an idea I have a project right now and I charge roughly 170$USD a day for very long term projects and up to 800$USD a day for single day projects. This is in Paris France. If I was in other places in the world it could be more or less. Just to give you an idea a little studio here is rented at 500$USD a month.
The per page or hour way of dealing with sites doesn't show very much professionalism to the client. Doing a few changes in the way you charge can :
1. make you more organised,
2. get more money if you are a fast worker,
3. make the client give you what you need when you need it.
4. look more professional towards potential clients.
I only work with contracts (a project in other terms).
Mainly what a contract looks like is this :
What I offer to the client,
What the client needs to provide for me to do my work,
What are the steps towards realisation of the goal (finished product),
How much I get paid for each step of the way (clients if they are in a hurry are sometimes ready to pay more if you do something fast, and actually sometimes penalise you monetarly if you don't give the work in time),
How much I get paid for each day the client does not give me the content or stuff I need to do the work with (yes you can do that).
I don't do all the work myself and usually had to deal with a couple friends (one a designer in the photoshop sense, another with databases). I sometimes hire my friends and make a profit for being the middle man (my friend don't mind since they make money and I can find work for them). I usually write a contract for my friends too so that they get what they want. If they fail to deliver because I charge enough I can always hire someone else to get the work delivered on time.
If you want to look serious you need a few things. References, a portfolio and charge so you make a considerable profit. You also have to be good at what you do.
If you are just starting out don't be scared to use that as your advantage. I started by making web sites for people I knew and did it for 20$/hr and often charged for less hours then I did actually worked. Now however my mother doesn't feed me anymore and I need to make money to live so I charge for every expense I can.
Hope this helps you out. Gary
Haran