I dry my pollen and anthers in small paper cups, it is very dry in the summer in the west. Then I pour it into plastic vials direct from the cup for freezing. Labeling the plastic vials is hard, I use first aid tape, long enough to stick to itself and then write on it. I used to use film containers for the larger stuff but those are not easy to find anymore so glassine envelopes would probably be the best bet for storage now.
I use paper matchsticks for pollination, they are disposable and can quickly be changed to a fresh one for each pollination. they are also biodegradable and will add a bit of sulfur to you soil so can be dropped.
I find that first thing in the AM is fin, pull off the anthers before they open, put them in a cut, label and they can be stacked in the tray when out in the field. As long as you are not collecting huge amounts they will dry in the paper cup just fine if you are dry and hot.
Brite mark pens do not fade, I used to sell them after testing every permanent marker I came across. Sharpie laundry markers will usually last the summer OK. Flagging ribbon is cheap and easy to use for marking crosses, do not get red, it will not last the summer. It is easily carried and ripped off for labeling and if you are doing several dif crosses on one plant you can color code if you get different colors.
Pollination caps can be made of foil by winding a 1.5-2inch wide piece of foil around a pencil and cutting sections off with scissors, this creates one open end and one closed end and it easy to put on the stigma after pollination. Just slide it down off the pencil end about 1 inch and cut, repeat. I stored the caps in a box to keep them from being crushed when in the field. I did all my pollination first thing in the AM and even before the flower opened, the pollen will still be viable for a couple of days after it is placed, longer probably when protected from the sun by the pollen cap.
I never had any problems with freezing and thawing pollen, but let it come to ambient temp before opening it, otherwise it may suck in moisture if it is humid (where I was it was humid at dawn). A frost-free fridge only seems to thaw on the bottom above the heat coils so I kept my pollen vials in jars in the door.
My method evolved from combining different methods from other plant breeders I knew or worked for so do what works for you and your conditions. The other thing you may try if your stigma is old and dirty is cutting off the end and apply the pollen to the style tube.
