Order for installation?

Unsure of what order to tackle this installation issue: husband and I have an older iMac with CS4 Creative Suite Design Standard installed on it. (He was a student when we installed it originally so we qualified for the student version, but I have read that we retain upgrade rights to a commercial version even now when he is no longer a student). We purchased the upgrade to CS5.5 recently enough that we qualify for the free upgrade to CS6, but we also bought a new MacBook Pro this weekend. Since we don't get the free upgrade to CS6 for 10 days, I want to go ahead and install CS5.5 on the MacBook Pro now because it has nothing on it. Do I need to install CS4 on the laptop first or can the upgrades run independently when you install them on a fresh machine? And will there be an issue trying to install CS6 on both a laptop and a desktop? Only one computer will be using the software at a time. Also, we own Lightroom 4, but since we have the new Canon Mark III camera, we need to use the beta 4.1 or 4.2 versions of Lightroom. Can they be installed on their own or do I have to first install the original CS4 version?