I'm looking to sell some designs and illustrations but don't know where to go. Big Cartel? Society6? Redbubble? Etsy? What do you suggest Designer News?
It really depends on the type of experience you want and how you'll be promoting it.
If you want to make a "shop" that looks how you'd like then Shopify is probably best.
If are just looking for somewhere to send people for them to buy, then a simple service like Big Cartel would be good.
And if you don't already have a clear sense of who would be buying them and would need people to discover your products on their own, a marketplace like Etsy is best.