Physical Fitness and Personality
I think there is a strong link between physical fitness and psychological/physical health (source). Physical attractiveness (body but not face) is also correlated to physical fitness to some degree (source). The more unfit you are the higher your resting heart rate and potential cortisol levels. Cortisol is a fight or flight chemical which if over produced inhibits mental functioning and increases the chance of a heart attack. There are numerous other chemicals that your body over or under produces when you have reduced fitness.
Aerobic/cardiovascular exercise increases slow wave sleep (the deepest, most restorative part of sleep), heart rate variability (which correlates to reduced mortality risk), and vo2max (the best current measure of aerobic / cardiovascular fitness), anaerobic exercise does not. Running is one of the best, most convenient cardiovascular exercises. A recent study in the Netherlands found that frequent running reduced mortality by a factor of 3.0 (frequent walking only scored 1.4). It would seem if you were going to choose just anaerobic or aerobic, aerobic is better at improving health / lowering mortality risk. However there seems to be some evidence that doing both is even better (source). Daily exercise is one of the few actualizable behavior traits that I've found to correlate to a higher Vital score on the MOTIVES test. The item 'I exercise every day' is associated (significant factor analytic score / correlation) with XOTXVXX on the MOTIVES system (i.e. high offbeat, thinking, and vital scores).
Ultimately, the best system is probably going to be whatever system you will stick to that is yielding some results (increased fitness / vo2 max score, better mood / energy level). For me, currently, it's one 3 mile a day run which is mostly aerobic (with the goal of improving my speed which has some anaerobic component, although just getting to three miles a day took over six months) and one set of pushups till exhaustion (more anaerobic as long as pushups are not super easy at which time I'll probably switch to pullups). Selecting three miles a day was influenced by a study that found twenty miles a week to be a sweet spot distance of running per week (source). If you are just starting, pick a distance you can reliably do every day no matter what (even if it's just a quarter mile), and increase slowly from there. Active recovery (light activity like walking) is also important for health in addition to more high intensity activity like running.