The Shackled City is a lot of fun but it's a slaughterhouse. Just as a heads-up, there are several places where you get bad guys that can easily TPK an unlucky or unprepared party. For example, there's a place in "Zenith Trajectory" where the party (6th level at this point) is hit by 3 EL9 encounters in rapid succession. There's also a lot of dragons (always a potential TPK if run well). Finally, at the high end there's lots of bad guys that can use blasphemy, and who will almost always be above the party level (no save, and SR unlikely to be of much good).
I'd highly recommend it, but with either a base party of 6 or with +1 the suggested level for each module. I haven't seen the hardcover yet but I understand they inserted another short adventure to help mitigate this issue.
Also, in my fictional treatment of TSC I kept the pace fast (and in the modules there are often long stretches where the party doesn't have access to stores/cities/R&R). I'd recommend adding some breaks for item creation and/or visiting "Sassarine", as suggested in the campaign.