I'll tell you my routine: it's a combo of cardio& strength that I love and has given me great results. 

Cardio: I run 4 miles twice a week, usually weekend mornings since it's getting dark early now. I also do 50 minutes of cardio 2 nights a week at the gym. The 50 minutes are broken up among different cardio machines: elliptical, stepper, bike & circuit training and treadmill. 

Strength: I do twice a week after my 50 cardio minutes. circuit training includes weights- so that usually covers me for one night, and is full body. On the second night I focus on machines that aren't included in the circuit and I rotate between upper and lower body. I do 2 sets, 15 reps per machine. 

Good luck finding a combination that works for you. 

The guidelines I posted are sufficient for health.  Beyond that?  I can't really help you with "what's the minimum I need to do to pass" because it'll depend on what intensity is enough for you.  

Going to the gym to hit your cardio goals is great too. Can I suggest something for home as well? Google DDP Yoga, it's "not ya mama's yoga" which has basic calisthenics  (using your own body weight to burn fat, build muscle and strengthen) and it doesn't feel like a chore to do.  

It starts with a beginners beginners and you can do 15 + mins a day in your own home at your own pace, nothing special required jus****ch it as a dvd or I think they even have an app.

I know it sounds like you dont particularly enjoy exercise at the moment, but I agree with everyone here, you have to find something you do enjoy and go from there. Telling yourself you "have" to do exercise vs "wanting" to be active is a big difference.  In the same way telling yourself you "have" to stick to that rigid diet in the long run didn't work.

Good luck and I think it's awesome you are looking at your options with exercise and hope you will keep trying until you find something that works for you both.

Thank you for your suggestions

The best exercise is one you'll enjoy.  If you go into this with the "We hate exercise" mentality, you will soon give up and stop going.  Since you hate it.  

Try figuring out what you will enjoy.  Maybe yoga and pilates are things that would be fun, or a BodyCombat class, maybe you'd rather do walks.  Maybe CrossFit would float your boat since there are metrics and fun things to throw around.  Experiment!  Try something for a month before you give up.  

That all said, find a trainer who is not only aware of body building.  An ACE certified personal trainer SHOULD be clued in tot he fact that different people have different goals and able to work with you to develop a plan that will help you reach your goals.  

That all said, to answer the question you actually asked, here are the activity guidelines for adults:  

Avoid Inactivity
Some physical activity is better than none -- and any amount has health benefits.

Do Aerobic Activity
For substantial health benefits, do one of the following:

• 150 minutes (2 hours and 30 minutes) each week of moderate-intensity aerobic physical activity (such as brisk walking or tennis)
• 75 minutes (1 hour and 15 minutes) each week of vigorous-intensity aerobic physical activity (such as jogging or swimming laps)
• An equivalent combination of moderate- and vigorous-intensity aerobic physical activity

Do aerobic physical activity in episodes of at least 10 minutes and, if possible, spread it out through the week.

For even greater health benefits, do one of the following:

• Increase moderate-intensity aerobic physical activity to 300 minutes (5 hours) each week
• Increase vigorous-intensity aerobic physical activity for 150 minutes (2 hours and 30 minutes) each week

Doing more will lead to even greater health benefits.

Strengthen Muscles
Do muscle-strengthening activities (such as lifting weights or using resistance bands) that are moderate or high intensity and involve all major muscle groups on 2 or more days a week.  [Specific time for this will depend on how long it takes you to work your major muscle groups.]