I don't know much about the mesh hats but I will answer the other questions.
Honigs has two types of flags that you can buy. (See here:
http://www.honigs.com/browse_products.asp?Cat=2&Sub=34 ) I own one of each, I keep the smaller one in my back pocket and the deep flag in my belt. This method seems to work fine for me. The deepflag in my belt is my primary and the one in my back pocket is when I have to throw it up straight in the air. Both are accurate but the deep flag can be thrown further.
As for the down indicators you should get one, everyone on the crew should keep track of downs. They also make two different types. (See here:
http://www.honigs.com/browse_products.asp?Cat=2&Sub=34 ) I have the one with the smaller band(f81), it is better because that big one will give you a more akward tan.
It's only 4 bucks so I would just get that because it looks a lot more professional than rubberbands.