ok, so you can keep the reader and fobs and choose an access system that supports Wiegand wiring (you will have LOTS of options). Those cards are most probably 26-bit standard and that will also be supported by just about every single access system out there.
Make sure to connect the wiring of the reader correctly to your new system:
The wiring should be shielded. The shield of the wire needs to be connected to an earth ground (NOT to the - of the panel) but should NOT be connected to the shield of the reader. The shield of the reader should be floating (cut it if you have to). The wiring should not be twisted on the D0/D1 line. If the previous installer used twisted pair for the reader, be sure that you use 2 wires that are not twisted together for D0/D1.