You don't need to hit the shops to get kitted out as far as clothing goes: a tracksuit in cold weather and otherwise shorts and a T-shirt are all you need.
Here are some pointers:
> Breathable fabric: Always go for materials that let sweat escape and keep you dry rather than absorbing it.
> Avoid prominent logos and detailing: The more fussy logos, the more likely they are to irritate and rub against your skin.
> A proper sports bra: You might not be blessed with DDs, but when you run they will bounce! Get a decent bra designed for high-impact sports that gives you proper comfort and support.
> Decent socks: Your socks need to fit your shoes - and your feet!- properly. Cotton is the most supple, comfortable material. If your feet get very sweaty, go for synthetic, wicking or waterproof socks.