For the "riding safely" part, just get caged
stirrups, and then you can get whatever running shoes will fit you well and not
worry about your feet slipping through the stirrups. If you don't want to
buy new stirruups, I'm sure you could rig your own cages with leather or
biothane strips riveted to the stirrups, or wrap the straps around the stirrups
and rivet the strap to itself, or a buckle arrangement if you wanted them
removable.
If you've never chosen running shoes, it's almost
impossible to mail order and get the size you need. Every brand is sized
differently, and you must choose a shoe for running that is larger than your
street shoe size anyway -- they must be wider and longer to avoid toe
bruising. Try to go to a dedicated runner's store and have an experienced
clerk assist you. You can go to www.runnersworld.com and search for the
article on choosing a shoe. For example I normally take a 9EE street
shoe, but I have running shoes in 9-1/2D and 10D depending on
brand.
I love the look of Ariat's styles, but they
obviously think all women have narrow B-width feet as that's the only width they
offer on everything, so I'll never be able to wear any of their
shoes/boots. Those Montrails at Sportack also have no width designation,
which means B-width only.