You can 301 from domain.com to www.domain.com; and you may find it useful to 301 from www.domain.com/index.html (or whatever) to www.domain.com - but only if you have a incoming links to www.domain.com/index.html, rather than to www.domain.com/

The seo risks of a relaunch are simply that a totally new site will be seen by the search engines as just that, which can be very damaging.

You need to preserve as much as you can of the 'old' structure - at least for a while, to enable the SEs to 'feel at home' and recognise that it is the same site; then new stuff will be assimilated fairly easily.

One possible use for 301s remains: You say it's a new website. But if ANY of it is the same as the old, but in a different folder/page, then a 301 from the old URL to the new URL will help. But as 'individual' 301s are labour-intensive, there's no point doing it unless the pages are pretty much the same.