Compared to the Charles Tyrwhitt Tailored fit, the TM Lewin fully fitted shirts are wider at the chest, but narrower at the waist. Thomas Pink slim fit is more expensive, but slimmer through the chest. You might want to try them. They have a sale on at the moment (at least in the UK).
From your measurements your waist size is larger than your chest size. Since Slim fit shirts tend to be more tapered and have a narrow waist, I think regular fit would be better for you.
In addition, from your measurements your arm length is shorter than standard, given your neck size. That means you are unlikely to find an OTR shirt that fits perfectly.
Go for a cotton shirt. Poplin weaves are usually thinner than twill or herringbone, so should be better in the summer. I agree with Trompe Le Monde, Avoid any polyester.
Many of the shirt retailers have a page telling you how to measure your shirts. Charles Tyrwhitt have a video on their website
The Charles Tyrwhitt Tailored Fit is Slimmer. For example, on a 16.5 inch neck
CT Tailored Fit - 45.7 at the chest and 42.9 at the waist.
BB ESF - 47.5 at the chest and 45 at the waist.
You can find more information here
for shirts your height and weight are less important than your neck size, arm length, chest size and waist size.
Thomas Pink have a guide here
If you provide measurements then we may be able to give you more precise advice on shirts that fit well.
+2 normally means that the sleeve length is two inches longer than the brand's usual length. For example, on the Thomas Pink website the long sleeve shirts are typically two inches longer than the standard lengthhttp://www.thomaspink.com/Men/content/fcp-content
For a 17 inch neck the narrowest shirts around the chest I know of are Thomas Pink. Both their Classic Fit and Slim Fit shirts are 45 inches. That's probably a little wider than you would like, but may be worth a try.