Neutronic and burnup characteristics of an accelerator-driven transuranium burner in a startup mode were studied. Different inert and absorbing matrices as well as lattice configurations were assessed in order to identify suitable fuel and core design configurations. Monte Carlo transport and burnup codes were used in the analyses. The lattice pin pitch was varied to optimize the source efficiency and coolant void worth while respecting key thermal and material-related design constraints posed by fuel and cladding. A HfN matrix appeared to provide a good combination of neutronic, burnup, and safety characteristics: maintaining a hard neutron spectrum, yielding acceptable coolant void reactivity and source efficiency, and alleviating the burnup reactivity swing. A conceptual design of a (TRU,Hf)N fueled, lead-bismuth eutectic-cooled accelerator-driven system was developed. Twice higher neutron fission-to-absorption probabilities in Am isotopes were achieved compared to reactor designs relying on ZrN or YN inert matrix fuel. The production of higher actinides in the fuel cycle is hence limited, with a Cm fraction in the equilibrium fuel being ~40% lower than for cores with ZrN matrix-based fuel. The burnup reactivity swing and associated power peaking in the core are managed by an appropriate choice of cycle length (100 days) and by core enrichment zoning. A safety analysis shows that the system is protected from instant damage during unprotected beam overpower transient.