"My first action would be to suggest we incarcerate anyone suspected of terrorist activity and every known terrorist sympathiser."
I'd be worried that "sympathiser" is rather too vague really. Would people who condemn the actions, but empathise with the motivations or some of them, be considered "sympathisers"? Would it rely on maybe one idle post, or would you not need a long-term pattern of "sympathising behaviour"? How long-term or not could that be? Also, wouldn't this amount to punishing people for thought crime? Aside from the moral implications of that, I'd have thought that you would just drive the sympathy levels up rather rapidly, only making the problem harder to deal with.
For the first part, I think there's a case for trying to move faster in arresting people suspected of terrorism, no doubt. The problem is that you'd still have to secure convictions, no? This has proven apparently difficult in the past, despite the best efforts of our security services (and for every failure there are hopefully plenty of unsung successes).
At any rate, incarceration without trial can't continue indefinitely, so there would need to be far more to the solution than that.