Weight Training, or perhaps phrased more accurately Resistance Training, is slowly gaining acceptance by more and more people, and has been proven by several different scientific studies to be one of the most efficient ways to help your body burn more calories, and assist in the calorie deficit needed to lose fat.
You don't need to worry too much about machines vs. free weights, and a valid case could be made that with proper usage, you'll get great results with either.
Remember: Anything you do is better than nothing you do.
Your best simplest introduction to the world of weight training is to focus on one body part or group for one half hour with 100 repetitions, or "reps". Your most important body parts are Chest, Back, Shoulders, Legs. The simplest, or best, exercises for you might be different than for some people, based on your body type, or previous injuries or other limitations, but the most bang for the buck, functionally, would be:
Legs: Squat or Leg Press
Chest: Bench Press or Chest Press or Fly
Shoulders: Military Press or Shoulder Press or Lateral Raise
Back: Pulldown or Row
Depending on what type of gym you go to or equipment you have, and working around your own physical limitations, pick something, anything, from the list. Unless you've done this before and have a good idea what amount of weight you can do safely, you might spend a week experimenting before you get started on this program.
Your 100 reps can actually be anything that works in a half hour. Sets x Reps: 10 x 10, 20 x 5, 4 x 25, 8 x 12. In fact, you could even set a timer on your phone (there are some pretty cool phone apps called "Tabata" or "Crossfit" timer that you can make work), and do 100 sets of 1 rep at 20 second intervals and still do this.
Remember: Anything will work for 3 weeks.
Every day except your one rest day, do the exercise from this list for that day in the same order for 100 total reps in one half hour, and keep the order for the rotation.
Example: Mon: Chest, Tue: Back, Wed: Shoulders, Thur: Legs, Fri: Chest, Sat: Back, Sun: Off
... and keep going.
You're going to ask about Abs or Core now, right? You're going to do that first as a warmup and not count it in the half hour. Just do three minutes of something that isn't a Circus Trick (if you're hanging on cables and rollers and look like something from Ka that's not appropriate for this phase of your training) before you start your main weight for the day. It's really that simple.
One of the most important aspects of this program is Logging. You need to Log your workouts.
You need to do 100 reps. If you can't at the weight or resistance (machine setting) you've selected, go down a couple notches and continue to finish out the half hour. Keep track of it and do better next time. If it's too easy and you feel like you could do 200, add some and keep going. Experiment. In the above example, notice I got done quickly, meaning I didn't need as much rest, meaning I could probably go up to 27.5 lb weights, or maybe try 10 sets of 10 instead.
Keep at it for between 3 and 6 weeks. This will build a great foundation for other, more complicated or more intense programs.
Let me know how it goes.