Kudos to you on the health aspect of wanting to drop some weight. I think most of us pick workout plans based on our individual goals and amount of time/energy we have available and are willing to commit to it. My own workout plan would probably be totally useless to you, as I'm trying to gain weight, so I won't share it.
However, I should echo what Nickofthenorth said: in addition to some weightlifting, you need to incorporate some notable cardio work into your plan, and also look at your diet. A combo of exercise and diet together does a lot more for most people than either alone does. Lower intensity longer duration cardio will probably burn more calories for you than trying anything too fast, so make your goals more along the lines of distance traveled/duration spent rather than speed at the moment. An mp3 player and a pair of headphones may well be a wise investment to keep yourself from getting too bored if you're doing your cardio indoors. Outdoors is more fun in nice weather, but it also runs the risk of leaving you far from home if you pull something.
Weightlifting will also help--more muscle will mean a higher basal metabolic rate, and will burn more calories for you even while you're not actively working out. To that end, it probably makes more sense to do exercises that involve larger muscles and more joints than isolation exercises--you'll get more bang for your buck doing squats than doing bicep curls in terms of total muscle development. If you have a substantial amount of weight you want to lose, it'll be a while before you'd be able to see definition even if you worked to maximize it, and that would probably get discouraging.
You might want to consider incorporating some exercises which you can easily do outside of a gym, just to prevent you from using the excuse that the gym's closed or too crowded--there's a lot you can do with pushups, for example, and a laundry detergent bottle or a large milk jug can easily become a light dumbbell when filled with liquid. If you find you're better about working out at home, consider getting a stability ball, and maybe picking up a few weights at some garage sales.
A few general tips:
Make a large number of small, incremental goals. If today you can only jog a mile before you get winded enough to stop, next time try to go 1.05 miles. If you can bike for 20 minutes today, try to press to 20:30 next time. If today you can do 8 reps of an exercise at 45 pounds, next time go for 9 reps. Or maybe 7 reps at 50. In any event, you want to make each workout just a little bit more difficult than the last; something that is fully attainable, but will keep you moving in the direction you want.
Remember that it will take time. Don't try to do too much too soon, or you'll make it really difficult on yourself and set up a strong possibility of failing. Don't try to go cold turkey into running 3 miles a day and eating a perfect diet--it's not going to happen. Give yourself at least one day a week off from exercise, and one meal where you totally ignore calorie content and eat something that you really want. This safety valve will keep you from feeling as deprived, and while it may make the effort take longer, it will make it easier for you to get there and easier to stay there once you've reached your goal. Fitness and health are long-term goals, not short-term ones.
Realize that set-backs will occur. They don't mean it's pointless to keep plugging away. Acknowledge that you missed a day at the gym, or cheated on your diet, that the past is over with and you're in control of the present and future, so go right back to where you left off and work from there.
Don't measure your progress primarily by your weight. Muscle's a lot denser than fat. Your weight might actually go up for a while you get into better shape. Pay more attention to things like how many flights of stairs you can take without getting winded and whether your arms hurt when lifting your groceries. To the extent that you care about the appearance effect of losing the weight, look more at the fit of your clothes. Are things becoming looser where you want them to?
As far as diet--I had a friend who lost about 50 pounds over a steady 8 month stretch of diet and exercise. Her husband lost about 40 in the same time period. Her two biggest pieces of advice were a) drink primarily water, possibly with a virtually-no-calorie flavor in it if you actually don't like water (there are a bunch of products out there that turn water into some form of ice tea or artificial fruit flavor for around 10 calories a glass), and b) eat nothing directly out of a container. She and her husband found that they went through a lot less junk food even without telling themselves that it was off-limits if they actually had to get up and get a second bowl of chips than if the bag was sitting within arm's reach.