Do you have a gym you can go to? That would help a great deal because of the equipment readily available. But if not, there are some exercises you can do with your own body weight. And don't be afraid of a little definition in your arms..when gaining strength you will see changes in your body. Not saying you will get very muscular (unless you shoot for that). Pushups come with practice. You can lighten the load by staying on your knees and doing them until you can do full form pushups. If you still find that hard you can do them on a set of stairs and face the stairs going up, this will make it easier as well.
Diet is most important thing in getting strong. You most fuel your body with the right nutrients to perform at its best..and also to help the recovery process. Buying some 100% gold standard whey protein will help your muscles recover by giving them protein quickly after a workout. Sometimes its hard eating after a hard workout and food digest slower than whey protein. Its the best choice for quick protein to the muscles. But you really need to pay attention to diet..because its the most important thing. It will directly affect your results working out.
As for exercises I'd recommend doing for a beginner like yourself (if your doing them at home) are pushups, dips, pullups...and squats. Legs are just as important because it actually boost your overall performance in your body. So while you do want upper body strength...you shouldn't neglect your legs. These are basic exercises and can be done with no weights. You can do squats with your body weight. If you find it to easy try doing 1 legged squats. Also do some cardio. 3 times a week is fine. This is just something to get you started and should help with over all physical strength that you are looking for...without adding to much mass. Stick to low carb diets and low calorie foods to avoid gaining muscle. If your trying to gain weight like me and build muscle..you would eat more than your recommended daily calorie intake...and eat plenty of carbs and proteins. Good luck and I hop this didn't confuse you lol.
Just do some research out there...there are great sites with workout plans for all body types. I will pm you the best one used over the years with real quality help that isn't some celeb bribe workout plan. It is an honest place and you can buy many different vitamins or proteins..and they have a forum for workout help.