MFP allots me 1200 cal per day, seems low?

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Hello,

I know there have been posts a about the 1200 calorie a day situation in the past, but I'm hoping people can offer advice with regards to my situation specifically.

I am 5' 6.5" and weigh 120 lbs. Since I'm in the healthy weight range, I'm not terribly interested in changing the number on the scale, but I'm what you could call "skinny fat" and carry extra fat around my middle. I figured in order to lose fat I should eat at a deficit, so I selected 1lb of weight loss per week, and selected lightly active since I am a teacher, which was one of the professions listed.

MFP gave me 1200 calories per day, and I eat back the exercise calories I burn. I've been doing the 30 Day Shred (a workout video with body weight moves like squats, lunges, pushups, etc) plus either jogging 30 minutes or doing 20 - 30 minutes on my elliptical 5 or 6 days a week. I enter the 30 day shred as circuit training 20 minutes, which gets me another 146 cal, while the running gets me 220 (even less for the elliptical). So the best I can hope for on a given day is 1500-1566 depending on what cardio I do. I know I should work out longer or more vigorously, but I am brand new to any kind of strength training and the 30 day shred wears me out.

Does eating 1500-1600 calories a day seem like a good plan for someone who is not overweight? I really want to lose inches more so than pounds. I'm not hungry all the time or anything but I'd like a little more freedom to enjoy something like a glass of wine with dinner a few nights a week. 1500 doesn't leave any room for little extras. Any recommendations?