The antenna is actually a fairly large inductor coil. The diameter and number of turns required should be enough to reasonably resonate with the capacitor at 125KHz. You get to choose both inductor and capacitor. From reading the data sheet, I got the impression they want the series resonant resistance to be about 32 ohms, and we get to choose the Q of the LC circuit which will then set XL and XC. I suggest a Q of about 500 to start with. Its just an educated guess for now. Perhaps 1000 might be practical, or perhaps these Qs are too high, I'm not sure. So, what value of inductance would give a reactance of about 15000 ohms at 125Khz? Once you calculate this, then calculate the capacitance needed to resonate with this and then you have Ca. Use a capacitor that is stable over temperature. Perhaps a plastic type, like polyester, would be a good choice.
Since this is a system that senses changes in the magnetic field when another resonant tank circuit (the RFID "tag") passes nearby, it makes sense to try shaping the antenna coil in such a way that these tags must pass through the coil for maximum sensitivity. In other words, make the coil large enough for people to walk through, like embedding it in the frame of a door. This sets the shape and size of the coil. You will have to figure out how many turns to get your inductance.
The value of Rv isn't clear to me, so perhaps some guessing is in order. This is a voltage divider to knock down the TX energy a bit, but the RX port can take up toabout 8 volts I think, and it needs a good voltage swing for sensing, so I would start with a value of about 4 times the internal resistance at that RX port.
Once the circuit is assembled and operating, you can experiment with other values to look for improvement.