For your very first period...no, you won't know...it just happens. After the first...or first several you should generally have an idea of when they will happen since they should become monthly. Most girls have pre menstrual symptoms which may include abdominal cramps, bloating, breast swelling...some experience facial breakouts, etc etc. No girls is really the same, and there is no exact set timetable for things.
And no, your period does not necessarily happen first or second, or third...there is no exact order of puberty changes happening. It is different for every girl.

I didn't know when my first period was coming. I was expecting to get it some time because I had started to get boobs so I knew things were starting to happen. But the first period just came out of the blue.
Once you have had a few you will probably begin to recognise the signs but they still sometimes come as a surprise with no warning!
And like BPP said, it's different for everyone!

if you have some signs of puberty it probably best to have some pads around just incase. But no real way of knowing when your first one could be, some girl (like every period in life) might feel things that indicate it's going to happen, others don't. And when it's your first you don't know what those signs are compared to just normal feelings of your body

I can only say for me, before I got my first period I had both breast development and pubic hair. Then about six months before I got my periods I began getting this sticky whitish vaginal discharge.
My mum bought me some pantyliners and told me that I would soon start my periods . Also getting closer I began to get tummy pains now and again
No matter how prepared you are your first period still comes as a surprise.

i second about carrying pads with you.
And yea you just never know. I lucked out and started while i was snug in my bed! I was both expecting it and not expecting it. Since i was a bit on the older end.

About a week before my first period, my mom brought me to the store to pick out a box of tampons and a box of pads. She put a couple of each in a pouch which she put in my backpack. She also put in a change of clothing.

I went to the nurse's office to take some antibiotics I was on. As I was sitting down as I was about ready to walk out of the nurses office, she noticed it.

Fortunately, I wasn't embarrassed and I knew it could happen anytime.

That is the only time that it ever happened in public or at school outside of the restroom.

When I was so irregular, I never paid attention to or really knew but it was coming.

After getting used to the pill, I knew that I was coming within days so I would be prepared.

I had no sign when my period came. not even the evening before. it just happened then.
but if you want to be absolutely sure that it doesn't happen during school and that everything is bloody, put pads in your panties