Merely reading these rituals will not make you a magician. The secret to success is repetition. Repeat the rituals until you can do them in your mind and you see the formless fire as though it were real.
When to use what?
Stenwick’s commentary on the “operant field” is particularly helpful here with his concepts of vertical intimacy and horizontal intimacy, but he leaves out the key to the whole thing – The pentagrams work on the horizontal intimacy and the hexagrams work on the vertical intimacy. “Within the column shines the six rayed star” isn’t just a nice mental image, it’s how it’s supposed to work. Please read his page, too.
When not actually doing magic…
When not doing magic to a specific end, the LBRP is the correct ritual to use. Think of it like sweeping the astral cruft out of your life. Astral cruft is stuff left over from rituals, thoughts about murdering that guy in traffic, worries about money, etc. The LBRH would also serve to clean out the mental cruft along with the low order nasties. It’s much better to understand you’re doing magic for spiritual growth, and use the LBRP/LIRH forms. Double banishing is the Big Reset button for magic.
When doing magic for mundane things…
LIRP is the ritual to use. The LIRP affects things which operate on the physical world. If I wanted a car and didn’t care how I got it, I would use the LIRP with the LBRH. Don’t overthink the results of these rituals, this is pretty much the template for using the Goetia.
When doing magic for purely spiritual things…
When going on astral tourism into the planes, scrying a tarot card or Hebrew or Enochian letter, or just trying to get information out of divination or similar, use the LBRP with the LIRH. This is also incidentally the form I use for most Enochian work.
When doing magic for mixed results…
For something like getting a job, you might need to change as a person to become the sort of person who can do that job, but the job is really a mundane task. On the other hand getting a good team together is often how well people “click” in addition to their skills. A job in particular is a good example of things which need to work on both the astral level (the team) and the physical level (doing the work). Use the LIRP and the LIRH. This is what I use for planetary magick.
Commentary on the Qabalistic Cross
The commentary page on the QC/KC should be more than enough to perform the ritual since the KC/QC is outlined and inseparable from the LBRP.
Commentary on the Lesser Ritual of the Hexagram
There’s as many opinions on the LRH as there are people doing the LRH…
Thelemapedia’s LRH Entry
Kraig’s The Map is not the Territory
Stenwick’s Wrapping up the Hexagram Controversy