The majority of scanners will cover 145.800Mhz as that frequency is in the ham radio 2M band and AFIK all scanners cover the 2M band.
Being a ham I have heard the ISS, shuttles, and even Mir many times.
It's quite common for hams to speak to the astro/cosmonauts on the missions. AFIK all manned space missions have a licenced ham on board, and most missions have their own dedicated ham callsign.
You do not need big antennas, usually the built in telescopic is good enough, but bigger better antennas will allow you to listen for longer.
On my chimney I have a weather sat receiving antenna, this is designed for 136Mhz, but it's great for ISS/Shuttle listening is it "points" skywards.
There are other frequencies to listen to, these can be found on Google.
Ususally the 2M frequencies are used for talking to hams or linking up with schools etc. A ham operator will visit a school, set up his station, and wait his turn. Most school hook ups are scheduled, but very often you'll hear the madness that we call a "pile up", as hams all over the footprints area start shouting.
I have never spoken to a mission, but I have had data signals transferred via Mir's packet radio node.
I remeber once when Helen Sharman was aboard Mir, listening on my 2M handeld radio one break time in work. My work mates were amazed that they were listening to the Mir space station!
Maplin sell a wide range of scanners as do Martyn Lynch +sons
and Waters and Stanton http://www.wsplc.com
Lynch and waters are specialists in the radio comms field, so a phone call to either will get you great info and good prices. I have bought a lot of kit from both of these dealers and can recommend them.
Sadly scanners have lost a lot of their appeal as the police are now digital, and mobile phones are GSM
...but the fire service and the utilities are still analogue, as are hams, taxis etc etc etc....
You can also use your scanner to receive the polar orbiting weather sats. This is superb! Live pictures from space as the bird flies overhead. Just listening to the beeps as it goes over is brill!!!! Receiving space transmissions is easy!