I know you asked for videos, and you have some suggestions there...but for the ultimate in free, you don't even need a video. Work your way through some of these, for example:
http://sportsmedicine.about.com/od/t...ictraining.htm
In terms of your particular problem areas listed:
Underarms - Not sure if you mean the actual underarm area, or the tricep area. For the muscles wrapping around your sides and in the underarm, pushups are awesome. If you're talking about the underside of your actual arm (tricep), dips on a chair are essentially equipment free and will work that area.
Butt ( I'd like to have more of one) - Squats, lunges, and all of their variations (Standard, chair, sumo, wall, and one-legged squats, front, side, back, and curtsy lunges). You can also do hip bridges, which can work hamstring and glute if you squeeze at the top.
Stomach (I'd like to have the muscles cut in at the waist and be flat on the front) - I firmly believe that abs are made in the kitchen. So that's more getting your overall body fat down, and as you said, you can't decide where it comes off first. But I love incorporating stabilizing moves into my lower body work (so for example, a back lunge into a front knee raise, which works your core because you have to balance on one leg and use ab muscle to assist in lifting the knee raise leg up).
If I'm not working from a video, I find it useful to build a workout in a written document (either in Word or on a piece of paper). I write out the exercises I intend to do in order. Usually I build my workouts to alternate between upper body and lower body moves, which means I can move faster through different exercises and don't spend as much time resting. This gives a greater calorie burn overall, resulting in overall body fat percentage decreases. So for example, I might do the following:
Squat
Lateral Raise
(repeat 1 set of each before switching back to the other exercise, do 3 sets total without stopping)
Rear Lunge with Knee Raise
Tricep Dip on Chair
(repeat 1 set of each before switching back to the other exercise, do 3 sets total without stopping)
Hip Raise
Pushups
(repeat one set of each...etc)
Chest Press
Chest Fly
Bicycle Crunch
Alternating Scissor
(repeat one set of each...etc)