What should the quality of my RNA be before I start building Illumina libraries?

Illumina recommends that you check total RNA integrity following isolation on the Fragment Analyzer, and look for samples with an RNA Quality Number (RQN) value ≥ 8.
Illumina recommends including a DNase step with the RNA isolation method. RNA that has DNA contamination results in an underestimation of the amount of RNA used.
Illumina does not recommend the use of low quality or degraded RNA with this protocol. Use of degraded RNA can result in low yield, over-representation of the 3' ends of the RNA molecules, or failure of the protocol.