Check out Picard suite for various quality metrics, CollectRnaSeqMetrics should cover most of your needs.

PS

FastX toolkit could be used for quality trimming, etc. It could also be accessed via Galaxy

You can run QC report using fastQC. It is java-based and has a user-friendly interface, don't need any programming skills.

In parallel to FastQC, common trimmers are trimmomatic, trim_galore (this is actually slow, but it works), and skewer...to name just a few. Some people also like using prinseq, though I have no experience with it.

I should note that I generally suggest people avoid the fastx toolkit. It's fine if you have single-end data (probably the most common), but causes no end of problems (and posts here) when people try to use it with paired-end data.

Picard , FastQC, etc are nice to evaluate your data previous to the mapping procedure

I would also include programs to analyze your mapped data with programs similar to Qualimap (you can use before and after the mapping), Statmap or similar programs

RNA Seq qc is also good

The most common modes of failure are are incomplete removal of rRNA (i.e. all you sequence is ribosomes, <~10% is normal, shows up as high alignment to rRNA), not enough input causing low complexity (shows up as high duplication rate which can be calculated but also seen in IGV - change the settings to show duplicates), contamination (shows up in low alignment rate), and sequencing your adapters rather than your RNA (shows up as low alignment rate)/

http://bam.iobio.io/ is BY FAR the easiest way to get your first quick and dirty stats.