I use cheap-o Next 'sports' socks most the time & they are fine, so long as you pull the ankle up high enough when you put them on.
My feet don't seem to sweat that much when cycling like they do when running - I am guessing due to the increased airflow at higher speeds & the fact your feet aren't really moving about inside the shoe as much.
However, I got a free pair of Bontrager socks at the 24/12 and they were pretty comfy. Probably be more comfortable on longer rides than my normal cheap offerings, but not sure if that's just because they are thicker.
If I got some thicker 'cheap' socks, they might feel equally comfortable.