Jina,
I think it's awesome that you want to start strength training--you're right, it IS important! It makes the body just *look* so much better as you lose weight. Not to mention all the actual health benefits....can you tell I'm a believer?
Sit-ups, push-ups, and the like ARE strength-building exercises, and I think that'd be a fine place to start. I know it can really be intimidating in a weight room, not knowing how things work, or how to do them. I'm lucky that I had some friends teach me/show me what to do early on in college, and I still use that knowledge now.
One thing you could do, is just observe the guys that use your gym, and watch how they do the different exercises. Then, when they're done on a machine, just try it yourself! As far as how much to lift, you can always err on the easy side by choosing a very small amount of weight, and add more from there. Do the exercises smoothly and don't use momentum to make them easier. You will see good results after a couple weeks!
Hope that helps--wish I could just take you to the gym and show you myself!
Jen