I fish in the central Sierras while backpacking and have fished along part of the JMT. I usually take a cheap (because I am hard on gear) spinning outfit with a small plano full of flies (grasshoppers, black gnats and black ants are popular and work well), a couple of those twist-on bobbers, and a selection of spinners, rooster tails, and a kastmaster.

Mind the regulations where you go - you will find yourself in areas where it's artificial lures only and barbless hooks. Wild rainbows in some rivers/streams in Yosemite are catch and release only.