I could suggest that there is *no such thing* as "short sleeve business very casual." But purely for the sake of this thread, I'll instead pretend that I've drifted into a parallel universe identical to my own in every way, save that very casual short sleeve shirts can constitute appropriate businesswear.
1. Polo shirts -
I'll put in a vote for Lands' End.
Literally dozens of different styles from which to choose - different fits, lengths, weights, fabrics, etc.
Good color choices.
No logo. I really dislike wearing logos.
And relatively inexpensive, particularly during one of LE's not-too-uncommon 40% off sales, or when using a really good coupon code. So even if the shirt doesn't last as long as an $50 polo from someone else - and I'm not saying it won't - at $18, it's still a bargain.
Go online. Buy a mess of (that's a highly technical term) LE polos in all different styles. Keep the ones you like. Return the rest to your local Sears for an easy refund. (I'm assuming you live somewhere near a Sears store. Maybe you don't. Maybe you live in some foreign land where Sears is unknown. But you neglected to say where you were located, so I figure I'm allowed to assume whatever I like with regard to your location.)
2. Non-polo shirts -
Go to Jos. A. Bank, or L.L. Bean, or somewhere, and buy a few seersucker shirts. Seersucker rocks. And since I'm pretending that very casual short sleeve shirts are business appropriate, I see no reason why seersucker should be ruled out.
I like seersucker so much more than madras, and seersucker will keep you cooler, and it actually looks better when it's somewhat wrinkled. It's a miracle fabric.