This is not a complete answer, as I don't really have time to write one at the moment, but I wanted to take a minute to address a few issues relevant to the contracting questions you raised in your post. (My apologies if any of this seems self-evident or is already on your list of things to do.)
Do you draw up a contract and what general things are contained in that contract (I'm not looking for legalise, just general things you consider)?
I'm sure you realize that web and web application design is a VERY risky business, for both you and the customer. If you want a better idea of what can go wrong from both sides, google "software design risk management." So, because this is a risky business you are venturing into, you need to take steps from the get-go to minimize the worst of the risk to both parties in order to have a successful experience. In particular, there are several points during the process where things could go wrong for YOU, and you need to be able to ensure that if that happens, your books aren't summarily put into the red or that you aren't put out of business altogether.
First, many clients will ask you to do a LOT of work up front before they sign a contract or advance you any funds. Sometimes they want you to go all the way to showing them a complete UI and working prototype before they pay. This is pretty unreasonable, from my point of view, because it puts all the risk on you should they decide they don't want to continue the project for whatever reason, or decide after a while to go with someone else to do the work. (It is even possible that folks like this may have several other design firms on the hook at the same time doing all this work before they make a decision. To my mind, this is like telling five tailors to make you a special suit and not picking which one you are actually going to pay for until the pants are just about ready to hem.) You need to decide how much work you are willing to do up front and stand firm or at least negotiate aggressively if pushed to do more than that. Standing firm on your terms and work is part of being professional, but it is difficult to do, especially when first starting out. There is nothing wrong, btw, with asking for some "earnest money" up front when starting a new project. Or at least, working that into the very early checkpoints with the client.
Second, you need to have some idea of how to set firm expectations of what you are planning to do for the client, and have that in writing and signed off by the client. You need to state your process for handling disputes and changes. If you do not have a "change management" process in place that you follow with your clients, you may find you've done twice or three times the work you thought you agreed to do by the time the project is over. Everyone always wants more, that's human nature. Once they see what you can do for them, you will probably get a lot of requests to "gold plate" things or add more functionality here and there. These may all be very small changes, but they add up fast into lost revenue. The key here is to have the project scope set out clearly and agreed to by both parties beforehand. I'm not saying you should turn down new work, just find a way to firmly tell them that you'd love to do that, but you need to finish what you contracted to do in the first place, because that's the professional way to do business, and then after that, you would be thrilled to talk about "version 2." ;-)
Third, some clients are slow to pay. Payment terms definitely need to be spelled out in detail in your contracts. As an example - I once worked through an advertising company that billed their clients NET 90 days. So of course, their clients paid on day 90 or 91, if not later. They expected to be billed on the same terms and not until their clients paid them. And, of course, the advertising firm paid their bills on day 90 or 91! So, if you can't afford to wait 6 months for payment of work done, be sure this is spelled out from the very beginning. I hate to say it, but when it comes to money, some companies will try a lot of really shady stuff to make their bottom line look good - at the expense of yours.
Finally, another way to cover your tail, financially, is to set up certain check points during the process, and have the client sign off on work completed to that point. And then bill them for it immediately. Make sure the client understand that this protects them, too - they don't have to pay before they see work they approve of. And, of course, it protects you, because you aren't waiting till the very end to get all of your money. That is always risky, risky, risky. But doing it this way, if they were to abandon the project in the middle of it, well, you're covered because you've billed and been paid for all or almost all of the work you've put into it to that point. Or, if they take your initial concepts and specs and then shop them out to a $2 an hour overseas web sweatshop, well, then you are covered for that much, anyway. It may be little compared to what you were hoping to make on the project, but at least you didn't give it away for free. (We won't go into the ethics or intellectual property aspect here.)
So, just some thoughts to consider on the contracting aspect. Best of luck!