Hi Don - the daisy chain might work, but unless you are reading data from the Base with the Arduino, I think you can just connect the Base RX to the Arduino, and the Base TX to the controllers. (Obviously everyone gets GND). You can also use Legacy SER2 modules to get as many serial ports as you need.
Remember that the Base/SER2/controllers use RS-232 voltages, and the Arduino serial port is TTL. So you will need an RS-232-TTL converter between them. You can make your own with a MAX232 chip, or buy a pre-made one.
For an RFID reader, I've used ID-20 readers. Each one can connect to a TTL serial port on the Arduino, and you can get 125khz tags in all sorts of shapes and sizes.