Advice on moving site to a new domain

Hi
Stupidly, I paid someone on fiverr to build me some links to my site back in December 2010 and July 2011. I haven’t done anything since, backlink wise and the site now has 47k backlinks – most of which are pretty poor yet all the content was written by me and is totally original.

I want to move my site as follows:
1. Move all the content from oldsite.com to newsite.com

What’s the best way to do this?
Delete or de-index oldsite.com after a few weeks? Or should I 301 it to newsite.com after I have moved all the content off it?

Sorry if it sounds like a noob question but I want to try and rectify my mistakes of the past.
Thanks in advance