I found that I can pick up a lot of planes even with the stubby antenna that came with the DVB stick. But I'm pretty close to the Heathrow flight path which gives me a slight advantage!
The dump1090 process uses 30-40% CPU on my pi so I start it up with nice -n+19. And it does seem to crash quite often so I've got something to check and restart it.
I built a small ADS-B Antenna out of Coaxial cable and even inside my Seattle apartment, I can track planes ~150 miles away.
You can also tap into trunking systems and decode NOAA weather satellite images.
Personally, I run dump1090 on a cheap TP-Link WR703N at home 
 - http://blog.y3xz.com/blog/2014/04/24/feeding-data-to-flightr...
^this guy gets about 500km coverage with the setup of antenna he has
What kind of hardware you need to get started? How does it track the planes, do the planes broadcast their info periodically? Hooking this up to a web frontend using Google Maps or Google Earth sounds like a very fun weekend project.
Oh, and a computer.
It's a pretty cheap way to get started with amateur radio!