Oh honey- try not to worry too much. You might find that your first few periods are really light and when it happens for the first time, you'll feel it before it starts running down your leg and causing an embarresment! You'll probably feel a thick discharge sensation 'down-there'- it feels tickly and sometimes comes with a bit of a stomach cramp. You'll feel a bit wet, as if you've pee'd yourself a little. Simply excuse yourself from wherever you are and go to the bathroom to sort yourself out. Chances are you will feel it before it becomes noticable to anyone else.
If it happens when you're sitting down and you get a period-patch on your skirt/trousers; tie a cardigan/sweater around your waist, as you get up to go to the bathroom. Unless someone is directly looking at your bottom, they won't see it before you cover it.
The likelihood is that it will happen when you're at home and relaxed. The body has a way of knowing when the best time is to start these things! Mine happened when I was 13 and at home relaxing in the evening. I can only ever recall one girl in our year having a bit of nightmare starting her periods, but she was only 11 and quite a well-developed girl for her age. She came on in class and it went through her skirt. She didn't notice, but the rest of the class did. I also recall us girls being very sympathetic towards her- it could have been any of us....and well, the boys didn't say a thing! Teenage boys and the conversation of periods don't go well together- they tend to avoid the subject at all costs! lol.
Unless your discharge is really heavy, I'd ditch the panty liners. You're prepared by carrying around the pads. Also, if you're really anxious about this and want to cover your ass (as the saying would go!), pack a spare pair of knickers in your bag and always have a cardigan or sweater handy to wrap around and cover any accidental stains.
The length of time for a period is different for each individual. It could last 2 or 3 days or up to a week. Most women get their periods every 21-28 days, but again, this can be different if someone is on contraceptive, has just started their periods, is going through the menopause or has a hormonal disorder.
When you first start your periods, it's not unusual for it to be irregular- you could come on, have a bleed for a couple of days and not come on again for two months or more. It could be that your first period lasts two weeks and then you come on again less than a month later. It can take a year or so for your periods to stabilise, but if they are causing lots of pain or they are having a real negative impact on your life, a doctor may advise going on a contraceptive pill to help.
For now, try not to worry- it will come when your body is ready. You're ready, so don't fret.
Good luck and best wishes
V