Terrified of Tornadoes

Hello!
Well, "terrified" is perhaps a bit over zealous. More like "reasonably concerned." We may be moving to the DFW area from the UK and we have 3 very young children. How much of a worry does anyone find the tornadoes?

I have visions of alarms going off in the night, not knowing what to do or where to go (simply "low ground in the middle of the house" seems a bit futile when you have a bloody great tornado hovering overhead). I've also started to get worried about what if one strikes the children's school. I'm not paranoid - just a mother worried about going from where this is zero concern to somewhere were it's a fairly high concern.

How do people find it out there? Know anyone who's had a run in with a tornado? Do you worry or am I just over concerned?

Thanks!