If you're going to use conventional products, choose those sold in the simplest packaging.
If your retailer doesn't carry organic tampons and pads, ask the store manager to consider adding organic products to the shelf.
O.b. tampons come in a small box with no applicator. They're compact, easy to use, and take up very little room in your purse.
Original-style Tampax are wrapped in paper and have a cardboard applicator which breaks down relatively quickly when exposed to the elements. They're highly preferable to the Pearl brand, which has a plastic applicator and is wrapped in coated paper.
For environmental options, consider:
Natracare - chemical-free, non-chlorine bleached biodegradable pads, pantiliners, and tampons. Available from whole foods and natural foods stores and food coops.
Seventh Generation - chlorine-free products made from organic cotton.
The Diva Cup - a reusable cup worn internally like a diaphragm. It may require emptying 2 to 4 times a day depending on your flow. This option generates no trash, but is not quite so convenient as a tampon.
Sometimes what you try is all about convenience. It's been a little easier for me to come by Natracare products, so those are the ones I'm personally most familiar with. I've been satisfied with them, but I can only get them at the food coop. If I'm at the grocery store and I'm in a pinch, I'll buy Ob or Tampax Original. Then I go see the store manager and ask him or her to order Natracare. Someday, maybe I'll be pleasantly surprised to see the low-polluting, chlorine-free, eco-friendly tampons sitting right there on the shelf next to the indestructible plastic-coated options!