Normally you want at least twice the size External TM drive as the internal, but in your case it may be 4-5 times as big.
PS. If your files are all that important, I'd do more backups/drives than just TM.
Also clearing older Backups will not help the space on the Internal drive.
How much free space is on the HD, where has all the space gone?
OmniDiskSweeper is likely the easiest/best, and is now free...
And if needed, you can use Terminal to run it in admin mode to see files/folders your user can't see...
My computer is indicating that I have limited space available and most functions will not work till I free space. ... I'm a photographer and cannot afford to lose recently added photos. Please help.
This could be a big mess for you. I am reluctant to suggest anything and have something go wrong with my advice and you blame me for making worse a problem that you caused yourself. So, I offer this suggestion at your own risk, but also encourage you to further research your options for a better solution by consulting your local Mac user group or a genius at an Apple Store, for example.
If your internal drive is so full that some operations are not working to the point of the computer being unusable, and you have a critical business need for that data, then stop using that computer and get a new bootable external drive. Maybe get 2 or 3 for extra backups, if you simply can't afford to lose that data. The more that you use the machine in its present state, the more you will continue to fill up the internal drive and risk corrupting data, if you haven't already.
Your "iMac" refers to many different models of computers from many different vintages, not sure what kind you have. Some models can boot from FW some can boot from USB, PowerPCs(G3,G4,G5) require Apple Partition Map, Intel CPUs require GUID. Some vendors' external enclosures are just plain problematic for booting Macs, a certain chipset is required to boot a Mac. Your best bet is to check with OtherWorldComputing for a compatible bootable external drive for your particular Mac. Note that you need an external drive that is Mac "bootable" not simply advertised as "Mac-compatible."
Boot from the Mac OS DVD that came with your computer and install it on the external drive. Boot from the external drive with the OS installed, then you can use the computer again without corrupting files on the full internal drive.
When you have a useable computer again running from that new OS on the new external drive, you can breath a sigh of relief and make another backup of the full-internal drive to the second external drive that you bought. Use Disc Utility to clone the entire drive, or something like Retrospect, CarbonCopyCloner, or Deja Vu. With this cloned copy of your internal drive on a much larger external drive, you should be able to boot from that one now and operate the machine again using the external drive.