Good grief, I think some posters have watched a few too many episodes of The Wire.
Mass gun killings are tragic but typically kill under 100 Americans a year, from a population of 330 million. You are highly unlikely to be a victim of gun crime if you (a) live in a good area (b) don''t own a gun - most gun deaths are suicides, followed by domestic/close acquaintance homicide. Unless you're planning to deal fentanyl on corners, you are highly unlikely to be the victim of a gun homicide by a stranger.
The risk of a US child dying in a school shooting is far less than the risk of a UK child dying in a traffic accident, but I imagine most of us still take our kids in cars without breaking into a cold sweat each time.
Not travelling to a good area in the US because of a fear mass gun homicides would be like an American reading about stabbings in south London and deciding not to come to the Stow-on-the-Wold. It's not that the risk in Stow is zero, but it's tiny.
The reasons I would hesitate to live in Texas, having lived elsewhere in the South are: (a) it's frigging hot and (b) it's a ball ache to have to drive everywhere. With the exception of a few older cities, walking is basically illegal in the States (only a slight exaggeration). Sometimes you can't get from a mall on one side of the road to a mall on the other side of the road without driving - nothing is set up for pedestrians.
There's loads of good stuff about living in the US though. Americans are just so friendly and welcoming (Presidents excepted..) that it's a great place to be an ex-pat. If the finances work and you're up for an adventure, go for it.