just a few points:
you will not build mass if you are not in a caloric surplus (taking in more calories than you are burning). if you dont want to gain mass, dont eat a lot.
for strength, the core exercises you should focus on are squats, deadlift (sumo or convention), bench, pullup ups, shoulder press (can be military press or push press style). other exercies work as well and keep the gym from getting overly repetative but these are what you should build strength workouts around. Also of note is that the squat and deadlift require extreme core strength. they will both build you core better than situps will.
in terms of rep range / weight, it depends on what you are comfortable with. the goal of strength work is to build strength, and you can do this in a number of ways but you need to push yourself. high rep to (or near) failure is good and is low rep high weight. i have found its mentally easier to force out sets of 3-5 than go for sets of 20+ reps so i like high weight low rep but its personal.
explosive movements are also good such as cleans, jump squats, etc.
lastly, focus on form. if you form is bad then you risk huring yourself. the saying "check you ego at the door" applies extremely well to strength work. there are a lot of, for lack of a better word, idiots that come into the gym and dont want to look weak. these are the guys that half squat 225 and wont touch their chest with the bar when benching because "its bad for your shoulders." man up, learn how to properly do each exercise through a full range of motion, and then start to add weight to the movement.
any questions let me know