If you go to the apple symbol in the top left corner and select " About this mac" you'll get a date for the machine. It won't be the exact date you purchased but a generation date e.g. late 2010.
If you are not comfortable with taking your iMac apart, and most people don't want to, then an external drive(s) is the best idea. You have a number of options, that in general depend on the age of the machine. This relates to the type of external interfaces you have. You will have USB, Now the only question is it USB2 or USB3. Not really a big problem as these are backwards compatible. USB 3 being the fastest. Again the age of the machine may reveal the type of USB you have. The other connection, if it's a non slimline version is Firewire 800. This is faster than USB2 but not as fast as USB3. Firewire was Apples preferred method of connecting drives for many years. Firewire drives tend to be more expensive than USB ones, and can be a little difficult to get hold of nowadays. You may have to opt for drives from GTech or Lacie who do combo drives which support multiple interfaces, including Firewire. I use a GTech GDrive on my iMac. it's Firewire and USB 3 I got it from the local Apple Store.