Paradise, you and I began with very similar stats and have very similar goals.
My path has been much like berryblond described - I started out targeting a higher number, but after a few weeks I found that I really didn't need that much to feel satisfied and energetic as long as my calories were coming from good, nutritious foods that I enjoyed. My target calorie range has been 1200-1500 since early February, and there are days I have trouble getting 1200 and days when I am hungry or eat calorie-dense foods and end up closer to 1500. My average intake over the past few months has been about 1250/day, and I exercise 5-6 days/week. Your plan to start with 1600 sounds perfectly fine to me.
I wouldn't even worry about the actual number of calories you burn at the gym each week - it's hard to know exactly how many you're burning unless you're using a heart rate monitor that tracks it, and the number of calories you burn doing the same types of exercises will change over time as your body learns to do them more efficiently. Just keep up with going to the gym, and the benefits will be obvious.
I was really glad to read that you'll be doing some strength training - I love the results I've gotten from it. As John suggested, make sure you're getting enough protein in your diet - it will definitely help increase your strength and prevent muscle loss. If you track your measurements and see small increases in some of them (like biceps or thighs) due to the strength training, don't stress and definitely don't stop the weight training!! It's a little weird, but because we can't choose where the weight comes off and are gaining some muscle, you can gain inches in some places even while losing weight. My upper arms had increased in circumference by an inch after my first month of strength training (I tend to put on upper body muscle pretty easily, and so saw a nice newbie gain), and only moved below my January measurements about a month ago. But in the meantime I got a lot stronger, and other parts of my body got much smaller.
Congratulations on your great loss so far, and good luck!