To measure a signal that has a typical rise time of 3-10ns you need to have a bandwidth that is high enough, the equations goes like this:
Bandwidth = 0.35/ Rise time.
Choosing the worst case scenario of 3ns, the bandwidth would have to be at least 117MHz. You would also need to sample at a higher rate than the bandwidth maybe 10 times higher so you would need maybe at least 1GS/s.
Something like the 3206A/B would be able to achieve this for 1 channel.http://www.picotech.com/picoscope-specifications.html
For 4 channels you need to go with a device like 6000 series , which can have sample rates of 1.25GS/s for 4 channels and have the sufficient bandwidth.:http://www.picotech.com/picoscope6000.html
The scopes can measure up to +/-20V and have a switchable input impedance of 50 Ohms (6402A/B,6403A/B, 6404A/B)
The 6407 is a digitizer and whilst it can do the same as the other 6000 devices it only has one voltage range which is +/-100mV, so the other 60000 series devices would be more cost effective.
This is all assuming that you want to see a 3ns rise time, but in any case this gives you the tools to understanding which product is correct for you.
Could you explain more about the problems you are having with the demo software, what settings have you chosen? what version of the software are you using as well?
Hope this helps.