There are many calculators out there that can figure out how much DPS increase a primary stat, a single point of crit chance, attack speed, and crit hit damage will do for your character. It is beneficial to take all of them into consideration.
Some skills only take into account of weapon damage, and not DPS. For that reason, you may want to consider average weapon damage instead. Using the monk's seven sided strike for example, even though a 1.0 attack speed 1k average damage hammer has the same dps as a 1.5 attack speed 667 average damage dagger, your SSS will do a lot more damage with the hammer than the dagger.
On top of that, there are many hidden attack speed thresholds for many skills that you may not know.
There are very specific IAS break points for many skills that can make a huge difference. For example, a WW Tornado barbarian or a Wicked Wind Wizard have specific target attacks per second for their main killing skills. Even though your dps character sheet might show that you are 'losing' some DPS, your damage output may be increased if you hit one of those breakpoints.
Some builds rely on having high crit chance, such as the popular critical mass wizard build so you may want to prioritize crit chance over crit hit damage.
Lastly, when considering a weapon, 'black weapon damage' is very popular as it comes into play when you have items that add % damage as elemental (such as the stone of jordan). That's why those tend to be more expensive. And this is also why cold damage SOJs are more valuable since a lot of people like it to add a snaring effect to their attacks.