So my question would be if I leave the SQL on the old server, would I just need to install another instance of CMS 7.1 on the new box and point it to the SQL server on the old box ? Also what about uninstalling CMS from the old box ?
First you'll want to setup a redirect for Agents, so that they can get to the 'new SMP server' without any real hassle or reinstalls required. Since the FQDN would be changing, this would have to be done to ensure they are automatically redirected instead of having to script out a change through a GPO.
Then you would install CMS 7.1 with the same solutions and versions (updates, SP's etc) as were on the existing server. I would recommend installing to a blank DB at this point, so that you don't cause any conflict with the existing DB or corrupt any data. Once you have that up and working (ie you can get into the console and no major errors), then redirect to the existing DB.
After you've redirected the new server to the DB and functionality is restored, you should be able to disconnect the old system and uninstall CMS.