This is an interesting issue because it's become so complex. To browse privately and still allow a website to function has become a difficult prospect.
You want each website to work, but you don't want any cookies or other data from one site to be able to be read by another. So individually sandboxed pages and cookies are the idea. Even if you block third party tracking cookies, other sites might be looking for cookies set by other discreet sites, not just cookies from tracking firms. The problem is so many sites use third party services for photo and sometimes entire article syndication that it's very difficult to tear everything apart. It's almost a case by case basis.
The worst offenders are news sites. Browsing with noscript, the list of third party URLs sometimes scrolls off the page. It can be difficult to pick through the content and find the correct one to enable an embedded video to play, for example.
For now I browse with noscript and adblock plus and occasionally private windows, but noscript is not an option for anything but serious enthusiasts who are willing to pick through all the trash to get what they want.
Browsing without an ad blocker and noscript on most sites is like sex without protection. You might be looking on that one day when a mainstream ad network has become infected with malware, and oops, you're fucked! I'm not against advertising but how you can trust any of it when so many ad networks have been compromised in the past, repeatedly?