You may want to keep things simple and try it with a regular omni antenna first. Very few passes go directly overhead, and many of then tend to arc low over the horizon.
Although not directional, you may want to consider home brewing a turnstile antenna. It consists of a pair of crossed diploes mounted 3/8 of a wavelength above a ground plane. The pattern is wide, and peaks around 35-45 degrees above the horizon- which is where many of the passes will be located. Gain goes down overhead, but it isn't a problem, as that's when the ISS will be closest and have the strongest signal.
Around 10 years ago, I used to work some of the FM sats mobile running nothing more than an HT, a 35 watt 70 cm Tokyo HiPower amp, and a Larsen 2/440 dual band mag mount antenna stuck on the roof! It took some planning and effort, but worked.
Also, please remember that since the space station is travelling at around 17,000 MPH, the contacts are extremely short, usually not much more than exchanging call signs and some short pleasantries. Most passes offer only a 5-10 minute "window". With so many other stations trying to work the ISS, attempts at long-winded QSO's can sometimes be seen as "hogging" the frequency.
73 and good luck, de Tom, KA1MDAwww.ka1mda.org