Payment arrangements (costs agreements) can vary from law firm to law firm. Best thing to do is let the law firm know how much you are able to spend on the case in total and whether you would prefer to make instalments as the case progresses.
If the law firm is happy to run the case by instalments, they will request that you deposit the instalments into their trust account. As the case progresses, you can request that the firm provide you with a copy of your account statement so that you can keep an eye on how the firm are spending your money.
It is uncommon for law firms to offer No-win, No-fee for matters other than personal injury. However, as above, each law firm varies on how they structure their costs agreements.