You do not need to upgrade your iMac to run TurboTax 2017. I would recommend that you download the latest release of Safari for the best experience running Turbo-Tax.
You also do not need to upgrade your iMac to High Sierra -ever - unless security updates are important to you. Many iMacs can be upgraded to run High Sierra (more memory and a solid state disc) but unless you're a hardware geek, I would recommend a new machine.
You didn't mention what OS you're running. Each Apple OS gets three years from launch with Apple supporting two prior versions in addition to the current. Based on Apple's current update schedule, support will drop in:
10.9 Mavericks - fall 2016
10.10 Yosemite - fall 2017
10.11 El Capitan - fall 2018
10.12 Sierra - fall 2019
High Sierra is an advanced 64 bit operating system. It will not run programs that were written for 32 bit operating systems. For more information suggest you contact Apple directly.
