Ohms - DC resistance, but for audio (AC) it's impedance.
High impedance - 300+ohm, you will need a larger voltage swing (in the 10s of volts, V) but less current (say 1-30 milliamps, mA), so lower power amplifier.
Low impedance - <120ohm, you will need a larger current swing - for example my 50ohm headphones are 60mA with about 2V max over them, a 32ohm will be higher mA.
The move from high to low is driven by the change in amp technology. Valve amps are good at voltage but not current - so that's why you see high impedance headphones used. Solid-state is good at current but not voltage so that's why you see low impedance headphones used with iPhones etc (they're easier to drive from a mobile device without additional inefficient power supplies for high voltage shortening battery life). There is a modern trend to lower impedance for this reason, 120ohm seems to be becoming a 'thing' being a between worlds but leaving the mobile lowest impedances alone.
Headphones with thinner wires tend to be higher impedance, they tend to offer faster movement being lighter but less bass. Heavier wires in low impedance tend to offer a slower movement and thus favour bass. Modern cans mean you don't have to worry too much about loosing the frequencies - but you do need to match them with the amp. In the end a good amp will bring out the best in your headphones and vice versa. I'm currently designing my own headphone amp/DAC from scratch. As you get more $$$ typically people are looking to trade on something to improve the characteristics they like in their music and may end up with a number of pairs of headphones for different music.
So the question is - what are you driving the cans with? A good set of cans will be an upgrade but you may find yourself wanting to upgrade the amp.. then the dac..
TL;DR:
Is it for use on the move? (size and ruggedness of the headphones, power requirements)
What music do you like listening to? (cheaper headphones typically focus on bass, without clarity)
Will it be in a noisy location? (closed/open back)