I want to run 100 feet of 10/2 wire from a 200 amp box using a 30 amp single pole breaker then into a junction box to connect to 12/2 wire then to a 20 amp GFCI to lights and outlets. Is this correct use of materials to go that far?

NO!

You have 2 choices. Use your 10/2 for your run from the panel board, but use a 20 amp breaker. Or use a 20 amp Breaker and 12/2 for the entire circuit

You must protect the smallest wire at it's listed amps, in this case 20 amps.

Not knowing exactly what you are planning to do, I'm a little concerned.

For example using a standard voltage drop calculator a run of 150' (end to end) the calculator says you need to use a #8 AWG feeder to keep the voltage drop to 3.5%.

The NEC "Recommends" not mandates that there be no more than 5% VD end to end.

The larger size cable reduces the end to end resistance of the wires. Lower resistance means higher amperage at the end of the wire for you to use.