Here we stress that diets are not the way to go, but you need to be willing to commit to a lifestyle change. It's great that you have a wonderful support group behind you, and of course you have us here as well!
Cutting the junk out is a huge first step. Like you mentioned, you need to get rid of the sugar and soda and any other junky food (fried stuff, chips, etc). More veggies and fruits are a good thing, but keep the fruit in moderation as fruit is ladened with sugar.
The most important thing you need to do for yourself is to create a calorie deficit, and what I mean is to consume less calories than your body uses in a given day.
Strength training is a must, but understand that while you are losing weight (with a calorie deficit), it is going to be very difficult to build muscle. The most important purpose of strength training while trying to lose weight is to maintain muscle, which is frequently lost during the weight loss process. The reason it is important to maintain muscle is because muscle burns calories, and if you lose muscle during the weight loss process in the end your body will lose some of its ability to burn calories and keep the weight off. This is the reason why so many balloon back up to a heavier weight than they started off at when they go through a crash diet.
Now, 3500 calories=one pound of fat. If you are hoping to lose 2lbs a week, you need to consume 7000 calories less than you use up each week, or 1000 calories less a day. In essence you would be shooting for a 1000 calorie deficit each day on average. You need to start counting your calories you take in each day, and subtract from it the amount of calories you burn (naturally and from exercise). If you set your meal plan up right, you can easily achieve this deficit you are looking for.
For someone of your weight assuming you're between 5ft and 5'6" tall, you burn about 2400 calories a day naturally. So, if you start off by burning 500 calories a day through exercise, you need to set up your meal plan so that you consume about 1900 calories a day.
1900 calories consumed-2400 calories burned naturally-500 calories burned from exercise= -1000 calories a day, or a 1000 calorie deficit.
To help you gauge your exercise and the calories you burn, 30 mintues a day of light/moderate weight lifting burns about 150 calories. You can also calculate the calories burned from cardiovascular exercise easily as most cardio machines will tell you the calories you have burned. I highly recommend cardiovascular exercise in addition to weight lifting as part of your regimen, that will really help you burn calories fast.