What should I be looking out for when moving to a cloud like Rackspace? Another user at serverfault had issues like compute cycles (CC) exploding and I did not want to have the same experience.
It looks like that issue that you linked to was less related to "the cloud" per se, and more to the admins needing to monitor their site and set proper permissions and caps. I use Rackspace Cloud Sites for some of my stuff, and if you wish you can cap the compute cycle scaling.
If you're moving to an environment like Cloud Sites, a no-shell system in which you upload your code, there aren't really any special considerations as far as "the cloud" goes, as long as you're using supported technologies (which for them is PHP, Perl, .NET, Python (I think), MSSQL, MySQL).
It's going to be very similar from the standpoint of your question to hosting on a typical shared provider, except that you have a discrete set of guaranteed computing power for which you've paid, and that capacity can be more flexibly scaled up through "the cloud" (meaning scalable clusters), if necessary.
When it comes right down to it, the easier your site treats the Cloud Sites infrastructure, the fewer compute cycles you'll generate. That's paraphrased from the documentation in the Cloud Sites FAQ.
There are quite a few things you can do within your application to reduce your compute cycles:
The more your dynamic application presents itself to the environment as static content, the lower your compute cycle usage will be.