A quick search online shows there are dozens of different types of hiking socks, with different materials, thicknesses, and properties. In general, what should you look for when shopping for hiking socks? What are the main differences, and what would make you choose one type over another?
Don't use cotton socks for hiking.
When your feet sweat, the socks become wet, and take forever to dry out. Good socks remove the bacteria and moisture that thrive in the environment created by sweating feet and help to prevent blisters. Cotton retains moisture, thus cotton socks will not do the job properly.
Rather, buy non-itching ("merino") wool, nylon, alpaca, elastic, polyester, spandex, or polypropylene(can also be used as a layer between the sock and skin) socks.
I wear wildland firefighting boots (all leather) for work, and they can take a long time to fully break in (6-12 months!), so a good pair of socks/combination of socks is crucial. I've found that I like to wear a thin sport sock under a full boot sock, which helps to add more padding and support up to the ankle, where it counts.
A very helpful source of additional information, including more information on the different benefits of different sock types and materials: Foot Care, Socks 101 & Sock Care.
I agree with everything StudioHack is saying.
Make sure the thickness is compatible with your hiking boots/shoes. It is a lot easier to add an extra sole to your boots/shoes to make up for some empty space. But, it is almost impossible to compensate for too tight a fit. So, either get socks first and take them with you when you buy boots, or take your boots with you to a shop that will let you try on socks. You may have to take an extremely thin pair of socks with you in order to do that.
I have used SmartWool socks for almost 20 years. I can attest that they are very comfortable (not itchy) and have kept my feet dry and cool in the deserts of Utah in over 100-degree heat. And, they keep my feet warm in sub-zero weather in the snow. So, I recommend them from may years of use. I thought it might be in my imagination that they worked so well until I used the Smartwool socks one day in Utah and cotton socks the next day. I cannot tell you how much better it feels to have dry feet in the dessert compared to wet, sweaty feet. I'm assuming that price isn't a factor for you. But, good gear (especially foot gear) is worth extra money. They run over $10 a pair depending on what style you choose - thick, thin, etc. But, I only use them for hiking. So, mine have lasted a long, long time.
Having said that, if you have never tried any brands, it might be worth while to narrow down your choice to a few brands, and they buy one of each and try them especially if you are planning to make a long hiking vacation. You want to try them out at home first, and then buy a number of the ones you like.
I did find that I could easily rinse out the SmartWool socks with mild detergent when I went hiking. I only had four pair. So, I had to rinse them for the whole week.