++1 on getting quality tires. When I started riding back in the 70s, tires were awful and flats were common. Now they are so much better.
13 miles is fairly long for a bike commute. I doubt you'll want to wear your office clothes - especially high heels - for that length of ride. Forget those picturesque images of Copenhagen or Amsterdam, those women are only riding 2 or 3 miles, at most. Inexpensive athletic clothing from TJ Max/Winners can work fine.
If possible, drive your intended routes very early in the morning before sunrise to see what sort of ambient lighting is about. If there are strong streetlights, you might be able to get away with those inexpensive clip-on LED lights. If not, you'll want to budget for something with at least 100 lumen output.
When the sun is low on the horizon, you'll need to think about whether oncoming motorists can see you with the sun in their eyes. Some sort of flashing light can make you more visible to them, or you can plan to ride earlier or later to avoid the problem.
Avoid cotton on damp days or if there's a strong probability of rain. I got hypothermia riding home in the rain in cotton pants and tee shirt once, years ago. Not fun. It loses all of it's insulating properties when it gets wet.