I am not a true distance runner..yet! Hopefully I am getting there. My first half marathon will be in Cape Cod in October and several of my friends are running or walking it with me. Joe will be walking and I am so excited about that. Lots of clam chowdah for us afterwards. I have been running regularly, but the real training is now getting started. My compression socks are just awesome. I love the colors they come in and they are not medical grade compression so they are easier to put on and pull off and give the lower leg a perfect squeeze. My legs are much peppier during my runs and the recovery after is minimal. I would recommend them for walking or running. The lack of venous stasis is really working for me. They theoretically should improve circulation during your run, hence more blood flow to your heart and lungs, more hemoglobin, more oxygen. They don't make me sweaty either as they are made of mostly polyamide and spandex.
These are my favorites so far:
CEP Women's compression socks
I have them in pink but they come in so many great colors.
2XU Women's performance run sock
I have them in the middle color, Peacock. These are softer than the CEP socks and a little less snug. Really nice to just have on in the house for post run soreness.