Help with strength

Try to follow a good strength program, like the book New Rules of Lifting for Women. In the mean time, there's a link to a routine on my profile page. I would do full-body lifting 3 times a week, and cardio on your non-lifting day. You can add a short cardio session after your lifting, if you feel up to it. Try to give yourself a day of rest per week.

First read this!
http://www.nerdfitness.com/blog/2011/07/21/meet-staci-your-new-powerlifting-super-hero/

Below is the content of a message I sent earlier regarding exactly this question. Some of it doesn't pertain to you, but I'm including it in case someone else needs it. The links at the end should be of special interest to you.

To weight lift for weight loss purposes, your goal for each lifting session should be one of two things. Either to lift as heavy as you possibly can for relatively few reps, or to lift a moderate amount for many reps rapidly. The first method maximizes muscle formation and the second is a form of weight based cardio that maximizes burn while limiting the amount of muscle catabolism (when muscle tissue is burned for energy)
Both of these routines can be done with either dumbbells, kettlebells or a barbell and plates, but in the case of the heavy strength day, you will probably quickly some to a point where your heaviest dumbbell isn't heavy enough for things like squats so if you have a little bit of money to spend, I would highly recommend a barbell with some plates from craigslist or a used sporting goods store. The prices range from very cheap to ridiculous, so shop around quite a bit. You will also want a weight bench with a squat rack on it. (See notes below)
Unless you just enjoy the environment in a gym, I am all for doing this at home, but first you really should get someone to watch your form on each of the major lifts until you are consistently doing them correctly. There isn't a single exercise that does more for your body than a proper squat, but practicing them incorrectly can cause all sorts of spinal injuries. They are safe when done properly! Which leads me to my next point. You mentioned machines in your message. I am all for machines to target a specific muscle if you are working on developing your physique, but for strength purposes they have a fatal flaw. If you are using a machine for, lets say, a bench press type activity, the bar is usually guided for you in at least one axis. This is great for targeting a muscle, but for building overall strength, it is leaving out all of the supporting and balancing muscles that go along with that one large, targeted muscle. What this means is that, if you have solely used machines for strength training, your large muscles will be very powerful, but all of the supporting cast will be relatively weak. So if you ever need that strength in real life, (to lift something off of yourself for instance) your secondary muscles wouldn't be able to keep up.
Free weights, on the other hand, require you to both lift and control the weight in all directions. This is more difficult to be sure, but it trains your entire body as well as causing massive central nervous system activation (which develops coordination, balance and steadiness.)
It doesn't really matter what program you follow for the strength days as long as you pick one which has built in progressions in weight (Starting Strength, Stronglifts and Madcow are some popular ones that can be read about online. I would probably suggest Starting Strength just because the guy that invented it really knows his stuff, but really just pick the one that you are most likely to stick with. I also know that starting strength leads you through how to choose your beginning weights for each lift.
For the lighter (NOT light, just lighter than the strength day) workouts, you should be trying to work at as high an intensity as you can manage. For an example of this, search youtube for tabata exercises or HIIT exercises. You can also use these days in between lifting to do some non-weight related exercise such as running, playing a sport, or some form of yoga or flexibility program.

Take a look at the information that I linked to below and let me know if you have any more questions!


Notes:

In no way should you just take my word for any of this! Please Google any terms or concepts that sound the least bit interesting to you. ("Deadlift Central Nervous System" without the quotes for interesting reasons why you need to do this exercise less often, for instance)

The bench I have cost less than $100 on Craigslist and looks essentially like this one: http://cdn.macolifestyles.com/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8d27136e95/d/s/dsc01025.gif

Helpful Links
Starting Strength Wiki: http://startingstrength.wikia.com/wiki/FAQ:The_Program

The Reddit Fitness FAQ (TONS of information):
http://www.reddit.com/r/Fitness/wiki/faq

The Reddit XXFitness FAQ (as above, but specific to women)
http://www.reddit.com/r/xxfitness/wiki/faq

The Reddit XXFitness Community:
http://www.reddit.com/r/xxfitness/

The Reddit Fitness Community:
http://www.reddit.com/r/fitness

Fitocracy (Like MFP, but much better at logging strength exercises. No nutrition component, but I like it to track my workouts more):
https://www.fitocracy.com