It depends very much on the subject & hardware used.
If you can tolerate the reduced depth of field a wider aperture is usually preferable, but at extremes this can get expensive & involve less highly corrected optics...
How high you can go with ISO depends a great deal on the sensor used some of my older cameras are effectively useless above ISO 400, some of my friends have cameras that do better at ISO 100,000. As the ISO is pushed up the image shows more noise. There are post processing options that reduce this effect & the acceptable amount of noise can vary widely.
Other options that might help on occasion are:
Extending your shutter speed 1/200 is faster than needed for most static/slow moving subjects (and not fast enough for some faster subjects). With image stabilization 1/10 can be usable hand held.
This street shot was fine at 1/125
P1140003 small by
Mike Kanssen, on Flickr
and this Infra red one in poor light doesn't suffer much from being at only 1/13 (though the contrast should probably have been boosted)
Rowhedge IR by
Mike Kanssen, on Flickr
Adding light is not normally practical for street/park shooting but a flash might be appropriate for your kids at the park. Changing the time of day you go out might give more light...
In low light aperture & shutter speed can still give good results at only ISO 200
Colchester Seige House by
Mike Kanssen, on Flickr
IIRC that was leaning against a sign post at 1/8s, f/1.7 with a camera released in 2006.
I don't often go wider than f/2 but it does happen.