If you are intent on keeping this one, an SSD is the only cost-effective and performance-effective path. It is not an easy upgrade but doable at home if you are careful. Believe me, the reward will be great without messing with your CPU or GPU.
If your slowness is in starting the computer and opening apps, but everything is fine once the app is running, that is a classic symptom of a slow hard drive, not a CPU, GPU, or RAM issue.
I have a direct comparison of what an SSD does. I have an entry-level MacBook Pro with a 2.5ghz i5 dual-core 3210M processor. We also have a 2011 iMac with a 2.5 ghz quad-core i5 2400S. As shipped both had slow SATA 3GB/sec mech drives connected to a fast SATA 6G/sec drive bus. The iMac's quad processor and discreet graphics made it a little faster than the MacBook Pro.
Both were slow to start up and to launch apps but ran OK once an app was running. The 7200 rpm drive in the iMac scored about 90-110MB/sec in read/write scores; the MacBook Pro's paltry 5400rpm drive struggled to make 70MB/sec. After adding an inexpensive 6GB/sec SSD from Other World Computing to the MacBook Pro, its drive scores are now 500MB/sec. That is close to a 10X data transfer boost. Although the MBP still has a less capable processor, in actual use it is now a pleasure, while the iMac with its old-school mech drive is a royal pain.
To show how that translates into the real world, here are launch times for my two slowest-launching apps on my MacBook Pro 2.5ghz as shipped; after doubling the RAM; and after the SSD upgrade:
Base system as shipped:
4GB RAM and slow SATA 3GBps 5400rpm hard drive: MS Word and Photoshop Elements took 15-18 seconds to be ready to use.
First upgrade, doubling the RAM:
8GB RAM and slow SATA 3GBps 5400rpm hard drive: MS Word and Photoshop Elements took 15-18 seconds to be ready to use.
Second upgrade, inexpensive solid-state drive
8GB RAM and fast SATA 6GBps SSD: MS Word and Photoshop Elements take 3-4 seconds to be ready to use.
Comment: ""Cost effective" is that, when the 2011 dies or is shifted on, you can remove the nice SSD, put it in an external enclosure and continue to use it as a backup or expansion drive for a newer computer.
Our 2011 is also a great computer but Mrs AJ uses it for our tax software and, next year, that software will no longer run on High Sierra, the max OS for that model. So we will have to go shopping regardless of what I put in her iMac today.
If I decide to experiment with an SSD in the 2011, I will be getting this "kit," That is important because anytime you replace the HDD in a 2011 iMac, you must install a special thermal sensor cable to keep the cooling fans from running at full sped all the time. The kit includes that cable:
https://eshop.macsales.com/item/OWC/KITIM11HE500/
If you buy a new iMac. do whatever is necessary to have the funds for the factory SSD, not the mech drive or the Fusion option.