Flexibility is one component of conditioning - the others are: strength, cardio-vascular fitness, co-ordination, and toughness. Flexibility reduces injury and increases the range of movement you can perform - by increasing the range of movement of your joints and the neuro-muscular natural free length of your muscles. Flexibility should be coupled with co-ordination and strength conditioning to facilitate technique - your body has to be able to support any movement you're trying to learn.
Flexibility in the absence of the other components of conditioning, is a very lop-sided and dangerous goal. The other components without flexibility and an understanding of it is, destined to shorten your career...
Endurance requires fitness (so you don't have to stop) and toughness (so you can't be forced to stop).
Toughness (physical and mental) is important. Work it out for yourself. [Please].
For primary fitness, try running, skipping, MA training at 80%, even aerobics. Add some sit-ups, push-ups, and maybe something like carrying something awkward, or climbing.
Back to Flexibility:
Brad Appleton wrote the stretching FAQ - read it! My caveats about his document (based on various sources, including Thomas Kurz's book Stretching Scientifically) is that the material is a little too demanding and has objectives too extreme for: beginners, older practitioners, and anyone recovering from injury. The basic principles are fine, but:
For a gentler introduction to stretching - and finding the feeling of good stretching exercises - try Hatha Yoga (eg, Iyengar) with an experienced teacher or group for about six weeks. Core strenght is also addressed (or should be).During training, there are stretching exercises as part of the warm-up. These will not provide much gain in flexibility for most individuals - and that is not their purpose, as they are part of getting the joints and muscles ready for hard work.
There is stretching at the end of class. This is a time for substantial gain - so long as the exercises are tempered with strengthening.
There is your daily morning regimen - where you loosen your joints, then muscles, with a minimum of stress - to find the extent of free movement of your major joints. Easy leg swings and held side-kicks are very useful. In particular, strengthen, and don't overload, your lower back. Warm up first.
Then there is specialised exercises (see the FAQ), but determine for yourself if you need more rest between sessions. Your muscles should feel quite comfortable when your movement is very near to your maximum stretch, and you should sense that you are very near to the limit.
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Tom Osborn - 1996, 2005.