Upgrade graphics card in 1st Gen Mac Pro?

Your only reasonable choices are the ATI 5770 or 5870 from the Apple Store. However, don't expect too much because these cards require a PCIe 2.0 slot for best performance. Your model only has PCIe 1.0 slots.

It can definitely be "worth it". But these cards can not reach their full rated speeds because of the Bus Speed limitations:

FIRST GEN SHOOTOUT:Barefeats tests Radeon HD 5870 + 5770 in
the 2006 Mac Pro versus older GPUs

With non-games, there is mixed results as well. When we ran Motion previews and Color playback, the difference between the two cards was minute. At $249, the 5770 just seems to me the sensible choice if you wish to extend the life of your "First Generation" Mac Pro.

As said before, adding the Radeon HD 5870 or 5770 to your 2006 Mac Pro won't cause it to "leap tall buildings in a single bound." But these new cards will help you "clear low buildings with a running start."

5770 in the 2006 Mac Pro

read the comments from users?

ATI Radeon HD 5770 MC742ZM A Apple Store

And to look at 2008-2010 performance:

Radeon 5870 vs 5770 GTX 285 4870

A small cautionary note:

ATI Radeon HD 5770 Mac Pro pre-2010

Some people have opted to also upgrade cpu with a pair of quad 5355 2.66 $400-500 if up to task.

I think Kappy is being overly conservative in "don't expect too much" remarks. You did not include what you hace in there now, to judge against.

Well, the cards support OpenCL which can improve render times since rendering is CPU intensive and OpenCL can use the GPU and CPU together to improve rendering speed. That being the case there should be some improvements if Cinema 4D supports OpenCL. This may make it worthwhile.

I have a 5770 in my 2006 Mac Pro. It replaced the earlier 4870 which replaced an even earlier 3870, etc., etc. No complaints.

I have, in fact, replaced my original CPUs with a pair of refurbished 5355s which should be cheaper today than they were when I did the upgrade.

It is definitely not a trivial task, and it does require some specific tools one may not have in their toolbox unless you do repairs on these machines. It cost me around $50.00 to buy the needed tools. Fortunately, there are a number of Google links that provide excellent tutorials on how to do the upgrade.

The biggest problem I had was loosening the RAM cage. I could not loosen the bottom screw which was apparently frozen or too well sealed to get loose. Made it difficult to move the cage sufficiently to remove the plastic cover adjacent to it.

Results were excellent nearly doubling benchmark scores.