at Jenny Craig when I was 300 lbs plus, they put me on an 1800 cal diet, and I lost at a good rate (it varied by week, lots of reasons for that). I'd say it's always been easy for me to underestimate the number of calories I eat. That means I'm usually eating more than I think, and I need to take that into account.
for me, a concern is if the calorie level is too low, will I mentally not be able to stick to it, then keep blowing the diet by getting too hungry and overeating (and usually turning to junkier food). I did 1200 calorie diet in high school when I was in the high 200s, and lost 100 lbs, that was pretty tough, and I was struggling with compulsive over eating.
in this last journey downwards

I started developing my exercise level at the same time that I changed my eating habits, I started with walking, now I have incorporated time at the gym. of course you can lose weight without exercising, but I really believe the exercise makes a tremendous difference for me, mentally and physically -- that's why I encourage it. there's a huge range of physically activity, I love to walk, and now I love the gym.
it's a good point that what you do one week may not show until one or even two weeks down the line -- that's been true for me many times. so if I work really hard, stick to the plan, sometimes it will take a week or two to show on the scale. and the inverse is unfortunately true, if I get lazy and eat too much, the gain may not show right away. and when I overeat now that I'm on a leaner, lower calorie diet, I can gain a couple of lbs of water weight immediately (which sounds contradictory, but my weight varies quite a bit from one part of the week to the next).
just a few of my thoughts!
good luck!!!