Born, a good place to start is 12 - 15 reps per set. That means you want to pick a weight that gets pretty hard somewhere between 12 and 15 reps -- like you really have to push yourself to get that last one out. If you get to 15 reps and still could keep going, you want to pick a heavier weight for the next set. But if you can't make it to 12, go lighter on the next set.
Start out with 2 sets of each exercise, 12 - 15 reps, and then you can progress to adding a third set.
The weight is going to be individual for each of us and, as Photochick said, it will vary from exercise to exercise. Keep the 12 - 15 reps in mind and experiment until you find the right weight for you.
It's a good idea to keep a training journal so you can track the exercises you do, reps and weight, so you know what you did the last time and you can watch your progress (which will be fast!)
If you keep a training journal, you can write your exercises like this:
DB curls: 2 x 10/15
Which means dumbbell curls, 2 sets, using 10# dumbbells, 15 reps. If you did the same exercise and did 15 reps on the first set and only 13 on the second, you'd write it like this:
DB curls: 10/15, 10/13
I agree that the New Rules Of Lifting For Women would be an excellent program for you and anyone else starting out with weights. You are going to love your results!