The technical term for a straight wire antenna is a "monopole antenna". The ideal size of a monopole is 0.25*wavelength. The wavelength can be calculated directly from the frequency of transmission as : wavelength( in meters) = 300/frequency( in MHz). Thus your wavelength is roughly 0.7m and 0.25*0.7 = 0.175m. Therefore a 17.5cm wire would be ideal for maximum range. As far as ground planes go, a good ground plane is always best. however just connecting to the circuit ground should surfice otherwise you can build a aluminium type one. You can on the transmitter side connect ground to the person holding the transmitter to enhance the ground plane significantly.