So to start the answer to your question; you want to monitor ISS, Weather satellites, MilSats etc.
OK well most of these are pretty simple to pick up. The cheapest method by far would be to get hold of one of the RTL-SDR USB sticks Welcome to the rtlsdr.org wiki! [rtlsdr.org wiki]
, these are < 20$. Add SDR# | A Software Defined Radio in C#
software to drive it, and you have a multimode receiver capable of tuning 60MHz to 1700MHz +-.
ISS downlinks in the 2M (145MHz) ham band just would require a simple hb9cv antenna for a good copy. You can look at something like n2yo.com for ISS tracking data.
Weather satellites; 137MHz, the SDR will be ideal for these since in software you can set the FM demodulator bandwidth to 30KHz +- then use something like 'wxsat' under Windows to 'decode' the APT signal into a picture.
Milsats; 240-270MHz, you probably want to build a simple Yagi (Satellitenwelt - 4-Element Yagi für 260 MHz
) or a helical antennas (UHF-Satcom.com - UHF antenna designs
). Again, the RTL-SDR will be fine for this as it covers the downlink band nicely.
If you don't want to go the SDR route, then pick up a 'real' radio like AR3000 from eBay, that has coverage up to 2GHz and is multimode. It doesnt have brilliant filters for weather satellites, but for everything else it will be fine.
Lastly, there is the #hearsat IRC channel, where you can come and ask any questions about satellite monitoring in general. You can visit StarChat IRC Network - Internet Relay Chat
and use the 'Java Chat Interface'. Simply put your name into the 'nick' field, and type 'hearsat' into the 'chat' field, then press the chat button!