Definitly DO NOT wear running shoes, it makes it way to easy for your feet to slip through the stirrups. If you don't want to invest in expensive boots yet, get a pair of hiking boots, that's what I used to wear. And when you get jeans, try to get some that don't have a huge seam down the inside of your leg, because it can really rub if you arent riding properly (or a beginner, and just figuring everthing out

).
I ride in either jeans or breeches, and have paddock boots/ half chaps for the summer, and tall winter boots.