R3-Flex

The card may not "reserve" memory, but it does use system RAM if required. Below shows what NVIDIA control panel tells me. Note that my two cards reserve the same amount of memory, indicating that NVIDIA's drivers will use up to 6GB of system memory for all GPUs as required, not 6GB for each GPU.
 
GTX 970 being displayed:
 
GTX 560 Ti being displayed:
Bear in mind that while the graphics card may not be specifically "32-bit" or "64-bit," if the drivers only work with 64-bit OSes, then that's all you can use it for. In the case of the RX series from AMD, 32-bit drivers are not available, and therefore will not work with a 32-bit OS as indicated by the below screenshot.
 
 

I had the same problem with my current GTX 1080.
 
What I did was to first uninstall all old Drivers with DDU (Display Driver Uninstaller). 
 
Then I made sure the integrated graphics chip was working while the new GPU is plugged in. 
 
Then while the new GPU is plugged it, but the iGPU of my 6700k runs the monitor, I installed the new graphics driver. 
 
Then it worked. 
Instead of using integrated graphics, you can also use your old GPU. 

You can get a gtx 950 for $90 off amazon with a mail in rebate.

I'm running a 750ti and i3 4350t off of a 100w psu, you will be fine

It doesn't. The required PSU thing is always waaay too much, 350W is more than enough.

AMD only has 64-bit options for downloading the drivers for the RX 400 series:
 

AMD hasn't released x86 drivers for RX4xx series
 
if your CPU is x86-64 capable, you'd have to switch to a x86-64 OS

Ya, go for an i3 6100
 
or maybe AM4 will be out by then