A numerical study of beam dynamics was performed for two injector systems for the proposed National High Magnetic Field Laboratory at the Florida State University (FSU) Free Electron Laser (FEL) facility. The first considered a system consisting of a thermionic DC gun, two buncher cavities operated at 260 MHz and 1.3 GHz and two TESLA type cavities, and is very similar to the injector of the ELBE Radiation Source. The second system we studied uses a DC photogun (a copy of JLab FEL electron gun), one buncher cavity operated at 1.3 GHz and two TESLA type cavities. The study is based on PARMELA simulations and takes into account operational experience of both the JLab FEL and the Radiation Source ELBE. The simulations predict the second system will have a much smaller longitudinal emittance. For this reason the DC photo gun based injector is preferred for the proposed FSU FEL facility.