On steady run days, try a mixture of surfaces. For quality days, deep sand is for strength or resistance training. It could include bounding for 20 seconds at a time, or reps of 1-5 minutes at 2 mile to 15K intensity depending upon which training phase you are in. As to shoes, you don't need anything special for sand or grass. Wet grass would be best done wearing non-road racing shoes because you'll need some decent gripping from the soles.
Trail shoes can be very specialized.
Few runners use trails rough enough to warrant the expense.