It's becoming common practice for web designers to create a separate 'mobile' version of a website since it's almost impossible to design a single site that works well on both a computer monitor and a phone screen. So, for example, The Answerbank uses this address for viewing the site at its best on desktops and laptops
http://www.theanswerbank.co.uk
but this one for for use on mobile devices:
http://m.theanswerbank.co.uk
If I was to design a website for use on desktops and laptops (because I've absolutely no experience of doing it for mobile devices anyway!) I'd probably opt for 'liquid page design' and set the width to '100%' (rather than to a fixed number of pixels). As a fall-back option I'd use 960 pixels. See here for the reasoning behind those decisions:
http://www.alteredimpressions.com/web-design/web-page-width-dilemma/