I'm a secondary teacher. My school doesn't require female teachers to wear suits or jackets.
I wear plain black Skechers Go Walks as I have plantar fascitis. They are great for standing up and walking / running around school all day - our building is over 5 floors as well so lots of stairs throughout the day. You can also sneak up on people in Skechers. 
I buy most of my teaching clothes from H&M, otherwise Zara and Mango. I wear skirts just above the knee with a shirt, or long sleeved top, or short sleeved dresses, with fitted, lightweight round or high-ish V necked jumpers when it's colder. Also opaque tights in the colder months (invisible socks in summer). Sometimes I wear a scarf too, most of mine are from White Stuff.
My colour palette is black / dark grey for skirts (also have one navy with windowpane check and one plum),
white for shirts,
white, cream and Breton striped for tops,
pale pink, dirty pink or blood red for jumpers,
and various colours for dresses including denim-y blue, pale pink, dove grey, blood red, black and white pattern, white with a pattern, and two that are Breton striped.
Don't buy too much at once as you'll take a while to figure out what you most like wearing and also what suits the temperatures of the rooms you teach / have meetings and assemblies in.