These have all worked for me without issue on the C1:
https://www.adafruit.com/products/1475
http://www.amazon.com/gp/aw/d/B00009MJKC
http://www.amazon.com/gp/aw/d/B003MTTJOY
http://www.amazon.com/gp/aw/d/B00I5SW8MC
Edit: Specified which Odroid iteration.
Not sure, but this is the one I use on my Mac and it works. It comes with a disc but you can install the driver online as well. If you don't find a solution, this is only $8.
What are you trying to do that the network adapter matters? I would say get the cheapest for your project’s budget, as long as it does what you need it to. If you’re concerned about firmware openness and OS support then those are additional requirements but I’m sure you could find something under $50 to meet those.
Edit - I realize that I didn’t answer the question. I’ll be back :)
Edit 2 - https://www.amazon.com/Edimax-EW-7811Un-150Mbps-Raspberry-Supports/dp/B003MTTJOY - I don’t know if you wanted wireless or wired. But this supports a lot. I’m sure there are more performant options but this tech has been around a while for compatibility. Don’t feel like you have to get it on the ‘zon as it was just a knowable link to get you to.
I have this one. I don't use it that often because it's mainly for my Raspberry Pi, but it works perfectly on both Windows and Linux in my experience with no drivers to install.
This is the one I use. It's an Edimax dongle ($10).
You're out of luck as far as newer wireless devices go however, incl. ones with antennas. I tried a bunch of them with no success.
I would avoid this unit because a) there are too few reviews and b) the technical details, like mfg or chipset are not disclosed it seems.
You will potentially save yourself a lot of hassle by finding a better reviewed and documented adapter. Any adapter that is advertised compatible with the Raspberry Pi will be Linux compatible. Example https://www.amazon.com/Edimax-EW-7811Un-150Mbps-Raspberry-Supports/dp/B003MTTJOY/ref=sr_1_5?s=electronics&ie=UTF8&qid=1531200156&sr=1-5&keywords=raspberry+pi+wifi
This is the one I use, it should be compatible:https://smile.amazon.com/gp/product/B003MTTJOY/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
To piggy back on this comment... I have sever of these floating around.. Works in everything I've ever put it in..
Edimax EW-7811Un 150Mbps 11n Wi-Fi USB Adapter, Nano Size Lets You Plug it and Forget it, Ideal for Raspberry Pi / Pi2, Supports Windows, Mac OS, Linux (Black/Gold) https://www.amazon.com/dp/B003MTTJOY/ref=cm_sw_r_cp_apa_RPOAxbXS7GBQV
Non-mobile:
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