1.
AFAIK, Honig's do not have any microfiber shirt, but they do have a cotton/poly (30/70%) blend. This makes it comfortable to wear even without an undershirt. Color is just a little bit different, but you really can't tell from a distance.
http://www.honigs.com/detail.asp?Cat=2&Sub=28&Item=216
Then they have a micromesh shirt, but there might be a rule in your assn. requiring the whole crew to wear solid shirts or mesh.
http://www.honigs.com/detail.asp?Cat=2&Sub=28&Item=211
2. Black undershirt. There are so many to choose from, and new ones appear all the time. Just stay away from cotton, but you know that already. This is the one I wear for warm weather: Ah, crap. Just some fancy flash site that makes it impossible to link directly to the product. Well, I'm sure you'll find something that works.
3. I wear McDavid compression shorts, 'cause I like the feel. When I tuck my shirt in, the stripes does not show through the knickers.
4. Generally, the more lightweight they are, the poorer the quality is. This is the ones I use, and they are the best I've tried:
http://www.honigs.com/detail.asp?Cat=2&Sub=32&Item=535
The regular ones are probably more lightweight:
http://www.honigs.com/detail.asp?Cat=2&Sub=32&Item=219
5. There are two different types, tube socks made of nylon and the fitted one which I believe is a nylon/cotton blend. The tube socks are the thinnest of course.
Tube:
http://www.honigs.com/detail.asp?Cat=2&Sub=30&Item=229
Fitted:
http://www.honigs.com/detail.asp?Cat=2&Sub=30&Item=230
6. Choice of hats has grown the last few years. I really like the "promesh" hats:
http://www.honigs.com/detail.asp?Cat=2&Sub=29&Item=698
Sounds like the promesh hat might be the one you should get.
There's also a new "flexfit" hat with something called "Cool Dry". Don't know if that's just a fancy name or not:
http://www.honigs.com/detail.asp?Cat=2&Sub=29&Item=871
Considering how much the actual size of a hat can vary (even if you order the same size every time), it could be a good idea to get one of those flexfit hats.
Good luck!