For turkey breast I would either smoke it or grill indirect. If it’s skinless, I’d smoke at 220-250*. With skin on, I’d grill indirect at 325* to help get that crisp skin.
For wood smoke I would use pecan which is fantastic with poultry, but hickory, maple, or the fruit woods would be good too. Those are all pretty mild in flavor, but you still want to be careful not to use too much smoke as you can easily overpower chicken or turkey with smoke, leaving too strong a flavor.
You may want to consider using a brine, which would help keep the breast from drying out and will also add flavor. Last Thanksgiving, I smoke roasted a whole turkey using a brine (first time using a brine) and it was the best turkey I’ve ever tasted. Had great flavor and was very moist throughout.