If she wants to use the kind of tampons with applicators, I suggest the ones with plastic applicators. They seem to go in more easily. I like the Playtex brand, although YMMV. Also, make sure she realizes that neither the applicator nor tampon is flushable.
If it’s difficult for her to get the tampons in, putting them in at a bit of an angle helps. I normally put mine in angled slightly down and to the side, but every girl’s body is different.
Also, O.B. brand tampons, which are applicator-less, are a little shorter than the applicator tampons, so I have an easier time with those. They may be slightly messier to get in, but I rarely have a problem with it. I like them much better.
If I were you, once your daughter decides what brand and type of tampons she likes, I would buy one of the packs that have the different types of tampons in them (light, heavy, regular, etc).
Especially before she gets used to being able to judge what heaviness of tampon she needs to use at what time, it might be a good idea for her to wear old underwear or very light pads during her period so that leaks don’t mess up her underwear. Heck, I still have leaks sometimes. I generally try to wear black underwear when I have mine- blood stains don’t show.
I’m going to second the idea of getting a cute little container to keep supplies in. When I was her age, I would have been mortified to have had to ask someone else for a tampon if I got caught unawares, or if someone had found one in my backpack. Menstruating was something that we all knew that we all did, but none of us ever talked about. I wasn’t comfortable with discussing on the subject until high school.
Tell her to begin marking the dates of her period on a calendar. This way, you can find a pattern. When girls start menstruating, a lot of times they don’t follow the strict 28 day cycle- if you find out she menstruates about every 20 days, or every 35 days, or whatever, she can better predict when she’ll need to be prepared for it. I always put a star on my calendar to mark the day when I was expecting mine, so that I wouldn’t forget and be caught unawares, and then wore light tampons for the few days before just in case it came early. Also, if she doesn’t follow an exact cycle, or is a little early or a little late, it’s okay.
If your daughter has any questions that she’s not comfortable discussing with you, I think there are websites and stuff that can help. If she wants, she can email me, if she doesn’t think it too weird to ask personal questions to someone her dad met on the internet.
I think it’s great that you can discuss these things so openly with your daughter.