The purpose of CUs and RUs is dramatically different. CUs are released about every 6 months and include a great deal of additional functionality in addition to bug fixes. The issue is that the codebase changes significantly, so regression testing for Production is a lot of work. RUs, on the other hand, are strictly a compilation of fixes for a particular CU. This greatly reduces the testing necessary and decreases the chances of running into significant issues.
At this point, CU03 seems to be the most stable (when running on RU03) with a variety of features, however CU04 was just released a few days ago.
To install the patches, review the OTM Administration Guide and the Patch release notes. The same patches need to be installed on all tiers (web, app, rpt) and the DB patch scripts need to be run, to ensure it is also at the same level. Failure to do so will cause a lot of issues -- just don't do it
--Chris