(Like all rules of fashion, these are general guidelines and are subject to season, weather, lifestyle, culture, geographic region, and personal preference.)

The shirt should match the occasion, and the collar sets the dressiness of the shirt. The tab collar and the rounded-collar-with-pin are the most dressy. The point, lay-down, and sculptured collars are most universal, and may be best for business. The spread collar is conservative, while the button-down is the most casual.

The collar should complement the tie, face and neck. Spread collars are better with a wide knot, and narrow lay-down collars are better with a narrow knot. 

French cuffs are more dressy than barrel cuffs, but they require cufflinks and are not appropriate for all occasions. Barrel cuffs are buttoned and are more universal.

Formal shirts are often made of broadcloth. Other fabrics include crepe, jaquard(which has a pattern in the weave); or pique(which has a fine waffle weave or impression in the fabric). The bib, collar and cuffs can be of a different fabric than the shirt body and sleeves. The collar is either traditional point, sculptured, or wing-tip.
 

Better dress shirts are 100% cotton. The quality of the cotton is indicated by the thread count: the higher the thread count, the better the cotton. The best cottons have 200+ threads per inch. Egyptian cotton is considered the finest cotton. Pima is a cotton derived from Egyptian cotton.

Oxford or pinpoint cotton is often used for the more casual button-down shirt. Broadcloth is smoother, thinner, and dressier, and is often used with the spread, tab, and point collars.