There are many aspects to website development agreement, particularly if there are to be on-going things for the designer to do once the site has been set up. The core issues that should be considered are set out as follows...
Functional Specification The Functional Spec defines what the software house is required to deliver. Approproate provisions should be built into the contract to ensure that the software developer has promised to deliver - the functional specification should delinate this work clearly. This naturally implies that the specification should be in writing - it is highly desirable to have a detailed written specification for your website agreed between you and the designer, so that everyone knows where they stand from the beginning. This makes sure that the designer knows what he has to do for his fees, particularly if they are fixed. You also need to consider what items may be extras and how much they will cost.
Registration of Domain Names Ensure that the web designer is obliged to register the domain name (if he/she is doing so) in your name, not his own name. Also ensure that you are not merely hiring the name from the designer.
Full Title Guarantee - Warranty Ensure that the contract includes a warranty by the designer that all content he/she supplies is free of third party intellectual property rights and that he will indemnify you on a "full indemnity basis" against any costs, claims and liabilities arising from breach of that warranty.
Assignment of Copyright Try and make sure that you get copyright in the site. It is reasonable for the designer normally to insist on payment before copyright is acquired. On larger projects you might like to include a provision whereby the copyright in material produced up to specific agreed milestones passes to you once the invoice for that particular milestone has been paid. This way you do not have a total loss situation if you fall out with the designer during the contract.
System and Software Performance and Legal Requirements Where there are particular legal requirements for your site, make sure that the designer understands these and make sure also that they are obliged to guarantee that whatever they have to do will work legally. You should not expect the designer to advise you or guarantee legal compliance but you should expect any specific instructions you give on that subject (having first consulted with your solicitor on the subject) to be followed and for that work to be guaranteed. This might include such matters as preventing orders being processed without the customer first accepting your terms of business using a pop-up window.
Maintenance Obligations Where there are on-going maintenance obligations on your designer, you need similar provisions regarding further developments of the site (e.g. regarding copyright, etc). Where they are also hosting your site you need to have warranties regarding security of information when taken from site visitors and also when it is stored by the hosting company and also when it is onwardly transmitted to your own servers/PC. You will also want some kind of service standard agreed for downtime (if they cannot guarantee their services are up at least 97% of the time in any given month you should probably look elsewhere) and response to requests for support and for handling emergencies.