Query about moving multisite to a public domain using www

Hi,

I have had multisite installed and functioning well on a dev site... It works on subdirectories.

twid.simplecsr.com
twid.simplecsr.com/demo
twid.simplecsr.com/template1

I have tried to move it to a new server (1and1) but have since been having problems with a few plugins (branding etc). 1and1 hosting has very limited dns options.

I have been trying to move it to:

http://www.twiddlejobs.com

Question:

When moving the site and updating the old references in the database wp_options, wp_blogs, wp_#_options etc should i be including the www in the database?

ie - where it said twid.simplecsr.com should i change it to http://www.twiddlejobs.com

If you could clarify the best practice here that would be really useful.

When it didnt work with www extension i removed it and just used twiddlejobs.co.uk which worked smoothly but is causing various issues with the login process.

Support access is open on the site.

(I have checked the download and moved the site on a like for like basis to a new domain shotyo.simplecsr.com and there it works perfectly. The only differences I can see is relating to the use of www and the different hosting providers server configuration)

Many thanks
Chris