Can I upgrade my iMac processor

Sadly you're between a rock and a hard place here.

You really can't upgrade the systems CPU to one of the newer i5/i7 chips and depending on what you have the highest version of Core 2 Duo your system can support is not worth the slight gains it offers.

While your friend is not far off going with a SSD. Your systems internal I/O ports are limited to one SATA port so you would need to pull out the drive you currently have and then the cost factor of a large SSD would bankrupt you as you need deep storage too.

OK, what to do...

I would recommend upgrading your internal HD for a SSHD hybrid drive like Seagate's as it also will run at SATA I or SATA II unlike most other drives you can get today which are to fast for your system.

Next I would max out the RAM the system will support if I remember correctly you can go to 8 GB if you update the systems firmware.

Other than that you may want to think about upgrading your system to a newer model.