Since I do not know the details of your family history of heart disease I answer with general recommendations. You should consult with your your doctor to make sure they are appropriate for you.
According to the WHO heart disease and stroke are (by far) the biggest cause of death.
In the book on brain health "The Brain Always Wins" Dr. John Sullivan states that "anything that is good for your heart is great for your brain.
Recent research seems to indicate that strength training is better for the heart than cardio, but the best is a combination.
The HUNT Fitness Study concluded that waist circumference or body mass index (BMI), leisure-time physical activity and resting heart rate are the most important factors for longevity.
They also found that the risk of dying from cardiovascular disease was 21 % lower for each increase of 3.5 mL/kg/min.
BMI is much simpler to measure than body fat. However this study concluded that percent body fat is a better predictor of cardiovascular risk factors than body mass index.
Another study concluded that muscle mass is a better predictor of longevity than BMI.
So for longevity you want to have a low percent body fat, high muscle mass and a high VO2 max.
Endurance training can ensure a low percent body fat but at the cost of muscle mass. A combination of endurance training and strength training can both ensure a low percent body fat and a high muscle mass.
Also long distance running may cause low testosterone, which in turn have negative health effects, whereas weight training increases testosterone and growth hormone levels.
I think it is little known that skeletal muscle has been identified as a secretory organ. This may have wide ranging implications. I am guessing that the healthiest in this regard is to have medium amount of musclemass.
The Cooper test was devised in 1968 by MD Kenneth H. Cooper as a simpler way for the US army to measure VO2 max of its members.
It consist of running as long as possible for only 12 minutes. This tells us that the focus of the cardio training should be to be able to run very fast for 12 minutes, not how long you can run.
Science is great. I think it is a good idea to also use common sense and caution. The golden mean dictates that you should do a bit of both cardio and strength training, but not too much of either.
Finally the Physical Activity Guidelines for Americans specifically states that adults should do strength training.