I have quite a few of the non-iron point collar blue and white shirts. They are a standard go-to item for me. I do not find they have a problem with breathability, and I get hot easily.
I would avoid the non-iron buttondowns. Those collars will never roll properly.
Check any patterned non-iron shirts carefully for a sort of plasticky feel to them. If it's present don't buy. It won't go away with washing.
On the other hand I've found some non-iron patterned and striped shirts at BB outlets that were indistinguishable from a standard fabric.
The ties are usually the 346 line - nice enough, but nowhere near as substantial as the regular ones. Look carefully, though - "Makers" ties do sneak in from time to time.
Slacks are nothing to write home about - good enough if there's a deal. I do have a couple of their "brushed twill" trousers that have worked out well.
In short, a crap shoot, but worth investigating if you happen to be nearby.
The fact that many SF's consider machine washing and non-iron shirts taboo is plain stupid. These people need to get a life.