The 3800 is a nice strong engine with plenty of low end grunt.
These engines had a lot of problems (intake manifolds burning or warping, cam sensor magnets dissolving in oil, coolant bypass tubes snapping, too much torque for the trans they're mated to) early on but by 2008 that was all dealt with. The supercharged 3800s could develop oil consumption problems, but with an NA version you're cool there too.
The only common problem you should be at risk of would be the little rod bearing issue they had. It was never really common enough to get fixed, but if you don't run Xw20 oil in it or race it you should be fine.