impedance and sensitivity go together so use them together.
sensitivity - how much decibel loudness output per watt of power input
impedance - resistance of the headphone circuit to electrical power
high impedance headphones also have greater control over the driver so generally sound better. not always, but as a general rule most high end headphones are high impedance.
generally high impedance low sensitivity = hard to power, high sensitivity = easier to power, higher impedance normally = harder to power but you cant always go by that since high sensitivity/high impedance are not always bad.
another thing to note, amp impedance. generally low impedance amps are best. some people say about 1/8 the headphone impedance or less is best but i'm not an expert on that.
frequency response will tell you from what hertz level frequency (think sound pitch, treble/bass) extents the drivers are capable of producing. keep in mind this does not tell you how they sound. while looking at frequency response numbers also look at frequency response graphs which provide a visual image. left to right is frequency (really low bass to really high treble) and vertical is weak response to high response (volume in db). for example a V shape on the chart indicates v-shaped sound with fun heavier bass and heavy treble audio signature while flat at 0 is a completely neutral can.
example here
http
/cdn.head-fi.org/c/cb/350x280px-cb811a2c_graphCompare.png
for headphones driver size is not an easy set in stone answer. it goes along with driver mass or weight. bigger heavier drivers generally are capable of better bass and are not as good on treble however this is by no means a solid rule (there are big driver low bass and small driver really heavy bass cans) so you can not really go by this to make a final call.
at 300-350+ you can often start getting into planar magnetic headphones like the he-400i. some planar headphones have good bass extension and better mids but some lack as much treble. they are often heavy. hard to say they are better than dynamics but certainly not bad. electrostatics are what stax and other high end headphones are and they are also considered good. honestly there are high end in all 3 (dynamic, planar, electrostatic) and all have good/ bad points. most of your headphones are going to be dynamic though.