Going into this, I knew NOTHING about rayon thread. Really, I didn't even know they made rayon thread. So starting from absolute zero, here is what I learned:
Rayon was originally made as an alternative to silk thread, so the look of rayon thread is going to be very shiny, and well, silky.
It is made out of plant fibers, and because of that fact, can be dyed in some brilliant colors. There is a little caveat to this abundance of hues, it fades and degrades, and will yellow with age. Bummer! :(
Light (ie: storing in direct sun light) and frequent laundering will both weaken the strength and fade the color of a rayon thread.
Another factor to take into consideration is that rayon thread will age and become brittle. To combat this you can either only buy thread for a current project (rather than stock up), and if you are storing rayon thread, do so in the freezer. Just make sure you completely defrost it before sewing with it.
Despite these downsides, rayon does have its place, and many uses. It is very popular as a machine embroidery thread and hand embroidery thread. It remains an affordable alternative to silk thread. And, if you avoid bleaching, and always launder on a gentle cycle, makes a very nice thread for sewing delicate garments.
One particular use I find for rayon thread is when attaching one of those pesky satin blanket bindings. The rayon's finish matches the finish of the blanket binding very nicely, and looks very pretty when done in a satin stitch all around the blanket binding.
I found a few spools of SULKY brand thread in my box, and low and behold, they were rayon! I had no idea what it was, and chose it simple for the aforementioned purpose. I love sewing with it, and it is not a very lint-y thread. One thing I have found, though, is that it is very, very weak. I don't even need a seam ripper to take stitches out with this thread, they rip out with just a little tug.
So while I like it for certain projects, anything needing strength, durability AND sheen, go with polyester or a silk finish cotton.
Hope this was helpful, I know I sure learned alot!!