When I began my little journey to fitness my stats looked a lot like yours. I'll share what worked for me.
5 to 6 days a week for 30 to 45 minutes
This will be something you will want to have as a goal to work up to. I would hate for you to burn out the first two weeks trying to get in the cardio 45 minutes of day and 6 days a week and lose your enthusiasm for it on the third week. Set a goal of maybe three days the first week of 30 minutes and then in three weeks add fourth or fifth day. In either case try to get it in as often as you can and as consistently as you can but always take a break at least one day a week from your cardio and certainly when your body tells you absolutely no. I also want to give a second vote to KAW suggestion to HIIT training. Again, more intensity, less time needed to do the cardio session and has a great "afterburn" or post workout increase to your metabolism.
3 days a week for now. Change your program every four weeks and aim for a lifting of goal of 4 to 5 days a week if possible.
To begin one set of 8 to 10 or 12 reps is about where you want to be. Eventually add a second set and a third in the coming weeks. Be certain to select a weight that is challenging to the point of near failure on the last two to three reps.
You will need to work all your major muscle groups. Lifting has been shown to increase your resting metabolic rate long after your workouts are over
It has burns fat too. Cardio isn't the only thing in our toolbox here. In my case, I really didn't notice changes in my body until I began lifting. Heavy. And then wow, let me tell you it was like I found the fountain of youth or something. Really. Lift the weights. I would suggested getting/using the manual that may have come with your home gym. There is also nothing wrong with augmenting with a few dumbells in my opinion either. Great places to start for an intro into lifting is http://www.stumptuous.com/cms/
Often the free weight(dumbell) exercises will also assist you in building strong core muscles if
you are using proper form/posture. Those muscles are the "girdle" that keeps your body in place while you lifting. Generally, shoulders pulled back and down away from your ears, and chin slightly up. Crunches are okay...
but more effective will be things that use more of your core such as planks and there are so many versions of these. Take a look at youtube for ideas.
Stretch! every day. Post workout is the best time and make it a nice slow stretch until you hit slight discomfort. Note how far your stretch is and hold it a few moments and see if you can take it just a little bit further in the next few moments. If not, try again the next day. This period post workout is important because your muscles are all warmed up and capable of a good healthy stretch. It also allows time for the blood that may be pooled in the extremities to return back to your head and core as well as help in the removal of lactic acid from your lifting session. (helps to be less sore the next day)
DRINK LOTS OF IT
It's 85% of success in removing unwanted bulges from the body. At least that's what everyone else has reported and researched. I agree it is very important and without a clean diet I was unable to lose the weight. But really, there is something that clicks when all three are done together: clean eating, cardio, lifting, they kind of feed off of each other. Eventually you may even look at a piece of food and think
Will this improve my workout for tomorrow morning, instead of the push and pull you may feel about wanting a piece of food but not wanting it to show up on your hips.
One thing I would also like to reinforce. YOU CAN NOT SPOT REDUCE. We did not eat something and decide it should go on our glutes. Nor can we dictate that this cardio session will remove the fat deposit on our thighs today.
Do the cardio knowing that it will come from where it will be come and just be patient with the process. It does work.
Now go get busy.