I just purchased an iMac 27" (late 2013) with the following specs:
3.2GHz quad-core Intel Core i5
Turbo Boost up to 3.6GHz
8GB (two 4GB) memory
1TB hard drive1
NVIDIA GeForce GT 755M with 1GB video memory
It's the latest low end model that Apple is currently selling.
If you have the same model then you can upgrade the 1TB hard drive with an SSD just like you can in any other computer.
I just finished installing 32GB of RAM from OWC http://www.amazon.com/gp/product/B00IELDDBA/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
and a 1TB Samsung 850 Prohttp://www.amazon.com/gp/product/B00LF10KTE/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
You will also need to purchase the right 3.5" to 2.5" SSD bay
http://www.amazon.com/gp/product/B00G56ZNZU/ref=oh_aui_detailpage_o00_s01?ie=UTF8&psc=1
Armed with a full suite of tools that I purchased from iFixit the whole job didn't take very long at all.
Just follow the instructions for replacing the HDD and installing the screen adhesive that's provided on the iFixit website and you'll be good to go.
The performance of your iMac will abolutely you!