OP:
Yes, you can boot and run the iMac from an external drive.
You can use either firewire800 or USB2.
Be aware that the bootup will be slower than if you were booting from the internal drive, but -- once up-and-running, the performance differences will be less noticeable.
However, get a -USB3- enclosure, it is backward-compatible with USB2, and when you get a new Mac, it will run at the faster USB3 speeds.
Here's an example of a such an enclosure:
http://www.bhphotovideo.com/c/product/1062440-REG/oyen_digital_u32_m.html
(I have one of these myself, runs fine)
Be aware that you can get an enclosure that has BOTH USB3 and firewire800, but they're more expensive than "USB3 only". Here's an example:
http://www.bhphotovideo.com/bnh/con...tSOvcgCFUiQHwodJ_UMqw&is=REG&m=Y&Q=&A=details
Then, find a 2.5" hard drive of sufficient capacity to put inside it.
I'd suggest a platter-based hard drive of about 1tb capacity.
I happen to like Hitachi, Samsung, and Toshiba.
Don't be afraid of assembling the drive yourself.
ANYONE can do this. If I could, you could.
This should give you "some more time" out of the old Mac, while you shop around and decide what to do next...