Weight Training?

When we diet we lose both fat and muscle. It's just the way our body works. If you diet and only do cardio you'll lose a good percentage of muscle and might end up unhappy with your results. You'll be thin but you'll have even less muscle and might have annoying fat storage in your belly, above your knees, love handles, even visceral fat among your organs yet your ribs might stick out and your arms will be bone-y. IF you lift while dieting you can maintain as much muscle as possible which will mean you burn as fat as possible. You'll have visible, partially defined sexy muscle. Fat storage will be at a minimum. You'll feel better and stronger too.

I know it's scary but I'd actually encourage you to go ahead and start with the free weights and skip the machines. Start with low weights. Pay very close attention to form. I'd recommend this program. It's only 5 lifts. Very simple basic, and compound (hitting lots of muscles at once).

http://www.myfitnesspal.com/topics/show/560459-stronglifts-5x5-summary

I'm with Rae and Mesha on this one. I've done it both ways so I can honestly say that the results are so much better when you add strength training to your fitness regime. I totally hear you on that not having much muscle mass part. I've always have disproportionately high lower body strength and almost no upper body strength so it was intimidating at the start. It was hard at first and, yes embarrassing at times, but totally worth it. Check out the New Rules of Lifting for Woman. It's actually a really interesting read and explains it all really clearly. Also, there's some stuff you can do at home to start out that will help with strength like pushups and pullups.

http://scoobysworkshop.com/zero-to-100-pushups-for-complete-beginners/
http://scoobysworkshop.com/pullups-for-total-beginners/

Good luck! You can totally do it.

It's very important - both in the short and in the long run.
The long run benefits include reducing your risk of osteoporosis, improved balance and thus reduced risk of broken hips (on top of having stronger bones), lower rates of reported back pain, and a partial offset of the slowdown in metabolism that naturally occurs with age. I can dig up links if you'd like to see them.

The short run benefits include looking way better than you can achieve by doing light cardio only. Because of lifting, I'm still about 10 lbs away from where I want to be, but I wear clothes that are 2 sizes smaller than what I wore when I was at my goal weight couple years ago. For the first time in 8 years I feel enthusiastic about wearing a bikini to the point of being obnoxious about it, and my legs and abs are absolutely firm.

Do not worry about starting from zero. Most people have to start from a low base and build up to it. If you work out in a gym, most people are so focused on their own workout that I highly doubt that anybody will notice how much weight you're using. As long as you keep pushing yourself a little bit more each work out, you will see good results.
I like the new rules of lifting book series. The new rules of lifting for women is a good beginner's book, as is the NROL for abs. A lot of people here have also had good success with Strong Lifts and Starting Strength.

When you first start lifting or incorporating strength training, your weight loss may slow down. Don't worry and don't freak out- it's just water weight because muscles retain water when you first start working out. In the first 4-8 weeks, a measuring tape is more useful than the scale because of water retention. Most people drop inches pretty rapidly during that phase, despite the slowdown on the scale. After the initial slowdown (which may or may not happen to you), you will start losing on the scale again.

ETA: Start as soon as possible. The sooner you start, the more muscle mass you can preserve. I second (or fifth) using free weights - there are tons of youtube videos that show you how to do exercises, and most gyms have trainers who should be able to help you with proper form.