A turbine engine is more efficient than a piston engine because it only has ONE moving part. No vibrations, minimal friction (no sliding parts). That is compared to the over two dozen essential moving parts in a typical 4 cylinder 4 stroke engine.
Although I have no real numbers, past automotive turbine engines run at 30,000 to 60,000 rpms.
Typically you would have an electric motor to start rotating the turbine's rotor. When the minimum RPM is reached, fuel is injected and ignited. Once operating temperature is reached, the engine can be throttled up to normal operating speed.
http://www.allpar.com/mopar/turbine.html
http://en.wikipedia.org/wiki/Gas_turbine
http://www.mtu.de/en/take-off/how_engines_work/