You may choose whatever propulsion you prefer, but need to accept the consequences. An electrical turbine is easy to build, but will need a lot of power for heating the core flow. Instead of burners you will need to install heater elements, which will necessitate a longer flow path and more volume between compressor and turbine, but by and large the electric turbine engine will look much like a fuel-burning one.
However, at speeds below Mach 0.5 propellers will give you more thrust per kW of power, and their efficiency is best at low speeds. The much lower energy density of electric storage will demand flight at low speed, or your flight time will be very short. Therefore, propellers are the best, but by no means the only solution.
A potentially even more efficient method might be ionic thrusters where a high voltage is used to ionize and accelerate air in order to produce thrust. Designs using ionic thrusters would use the whole airframe for thrust creation and would need to be run at tens of thousands of Volts, but their potential efficiency surpasses even that of low-speed propellers - in theory. The linked article, however, is an embarrassment to MIT. A 1 kW jet engine that produces only 2 N thrust has to fly very fast (500 m/s, to be precise) while the 110 N cited for the ionic thruster at the same power mean that it could not had moved faster than 9 m/s.