OK, this test sounds totally doable, even if you don't happen to do well on your first assessment next week--you've got plenty of time to make up for it.
Realize that I am in no way a professional in this. Check with your doctor if you have any question about whether you are ready for an exercise program.
Those preliminary results will give you a good baseline to work from, so you'll have a chance to figure out what in particular you need to pay attention to.
For the step test, you'll be working on basic cardio fitness. That, incidentally, is also important for you if you decide you want to lose some weight, which might make moving around in your costume easier.
The strength parts of your test are fairly general. Since they won't involve huge amounts of weight--the greatest weights you'll be dealing with will be your own body weight--you'll be able to work on them without even needing huge amount of equipment.
Since you really are new to this, I would advise not trying to do too much too quickly. If you try to jump in too deep and go straight to, say, an hour a day 6 days a week, you'll increase the odds of failure.
Picture. Take a picture now. This is your before. Even if you don't want to show it to anyone at all, take a picture of yourself shirtless. You will really, really want to have one once you've gotten yourself into a shape you're happy with. There's nothing quite like the mental thrill of "This is what I used to be. Look at me now!"
Cardio. You'll want something like half an hour of cardio, three days a week to start. Don't panic if you can't jog for that long right at the start--jog for as long as you can, and then walk the rest of the half hour if you have to. If the first time out you only make it jogging for 12 minutes, work on grinding out an extra minute the next time. And another the time after that. Mix up your cardio if you start to get in a rut--jogging, biking, swimming, climbing stairs, elliptical machines, rowing machines, a jump rope, step aerobics, whatever you need to make you move and get your heart rate up. Ideally, you'll want to be somewhere in the neighborhood of 75% your max heart rate, which should be 220 - your age. An mp3 player will make it much easier to make yourself do this. Be sure to stretch when you're done.
Strength training. At this stage, I'd say you're better off doing a whole body routine 3 days a week, rather than breaking into different routines for different body parts. Pick a small number of exercises, and learn how to do them with the best form you can. There are videos on this site showing how to do essentially any exercise you want; at a gym, you can also ask staff members how to do something to ensure you're not going to hurt yourself. That is part of what they are there for. Exercises I would recommend for you:
Tricep Bench Dip.
All of these rely on body weight, rather than free weights, so you won't be able to make any excuses about the gym being too crowded or not open at convenient hours. In fact, the only one that really needs any equipment (other than a chair or bench for the bench dips--if need be, you can use the edge of a bath tub) is the chin up. For that, you need a bar that you can grasp and pull yourself off the ground. If you can't find a convenient one, they sell adjustable bars you can temporarily fit into a door frame for that exact purpose.
If you're going to be using a gym for the strength training, you can use some weights or machines if that's important to you. For the tests you list, you'll primarily need strength in the legs/rear (for the stepping and the wall sit), and the chest/shoulders (for the pushups, primarily, but shoulders also for the arm extensions).
In general, strength training, particularly with weights, has a trade off between the weight you move and how often you can do it. A low number of repetitions (say, 5 or 6) will allow you to use the highest weights, and is used for developing pure strength. A low weight on a high number of repetitions (say, 12 to 15) will do more to help build definition. Intermediate values of 8-10 will balance the two. You will want to adjust the number of sets you do such that you're in the range of 20-40 total repetitions for a given exercise.
Keep track of your progress, and be sure to adjust things as you improve--add to the weight, add to the repetitions, go for a more difficult version of the given exercise. You need to constantly challenge yourself, or you'll stop improving.
As for your diet, the basic formula you'll care about is calories eaten - calories burned. If this is a negative number, you're going to lose weight. If it's 0, you'll maintain your current weight. If it's positive, you'll gain weight. Take a week or two of what you're eating now and track it--you can set up a free account at www.fitday.com
for instance. If your weight is stable, that's the also the amount you're burning. To lose weight, you'll want to increase your activity level and possibly lower the absolute number of calories you eat. Do not try to operate a daily deficity of more than 500 calories. 500 calories a day in difference is enough to lose a pound of fat in a week. 6 months at that level (meaning late February) would be 25 pounds of fat lost. From your profile weight, if you are currently at 30% body fat, 6 months would get you down near 21%. That's a third of the fat on your body. There are lots of articles on this site about how to alter your diet, but the essential advice is to eat a larger number of smaller meals so you don't have huge variations in your blood sugar over the day. Find the substitutions you find easiest - 1% milk instead of 2% milk, diet pop and water instead of sugared pop or juices, whole grain bread and pasta instead of white. Don't be too strict with yourself though. Overly strict diets are an invitation to failure, because you will inevitably break them. Think more in terms of "gradual lifestyle change" than "must lose weight by next week". One meal a week of whatever you want should be enough to keep you from feeling too frustrated, yet not be so much to ruin the effect of the rest of the week.
If you're feeling really ambitious, there's always the RealJock Strength Foundation 12-week program for beginners
. I would recommend holding off on that for a month or two, until you get very used to going to the gym regularly anyway. 12 week plans are a bit ambitious when you're first beginning.
Keep us posted on your progress, and don't be afraid to ask questions. Good luck.