Mini ITX Gaming/Streaming GPU Choice

You can fit more or less any graphics card in a Prodigy by removing the upper drive cages. In this scenario you still have enough space for one 5.25" drive, two 3.5" HDDs and up to 4 SSDs, all at the same time. That's plenty storage options for most people so the top drive cage usually goes for extra graphics card space and better airflow. The main limitation is actually width (it's kinda strictly double slot) as some cards are slightly wider than dual slot which might present problems.
With the cage removed, you have 330mm of clearance. To put this in perspective, a GTX690 is around 280mm, the Nvidia Titan reference cooler is about 267mm and the Gigabyte G1 Gaming GTX970/980 comes in at 312mm.

My advice - pick whichever is cheapest or whichever you have a preference towards. I'd personally skip both the Zotac and the EVGA. The Zotac is aesthetically a bit dull and seems a bit outdated in it's design which might go some way to explain why it's so reasonably priced. Given the GTX970 doesn't need huge amounts of cooling, I'm sure it'd work fine regardless. The EVGA cooler got some bad press this time around due to confusion over whether or not a backplate was provided and how much contact one of the heatpipes made with the GPU (not a lot).
Based on current US prices I'd probably pay the extra for the Gigabyte Windforce, MSI Gaming 4G or Asus Strix versions. It's an extra $20 but all are well reviewed and all have a potential USP - the Strix for example has a decent claim at being the most quiet.


General build advice. You didn't list which Prodigy version you are getting but I'd avoid the side-window versions as they really nerf the graphics cooling potential. The rest of your build looks fine but I'm not 100% sure where the 120mm fan comes from. You only really need two fans to cool a Prodigy effectively (front+back) and with an ODD in place you remove completely one of the top locations and potentially block the other with cables. I'd just skip trying to put a fan here anyway, I've done a bit of testing myself and never managed to influence temps by putting roof-fans in my Prodigy(s). On the subject of fans, I'm not sure how good the Spectre 230mm is. The stock Prodigy fans are Spectre 120s (not the Pro versions) and they are very quiet but kinda basic in design and don't move a load of air. The Spectre Pro series, by comparison, move significantly more air at the same RPM but there is a trade off for noise. As I assume you aren't overclocking, then a lot of this is kinda moot anyway- you don't need much cooling.
That brings me to my last point - the i5-4690. You've matched an overclocking chipset board with a non-overclocking CPU. I wouldn't buy one as it's (arguably) the worst value i5. At stock speeds any standard i5 will perform very similarly as they only have 0.1Ghz intervals between models and minor differences to the turbo function.
I'd either get a 4460+H97 and save $60, you'll never notice the difference OR get a 4690K (it's possible this was your intention) and a decent mid-range tower cooler in the Hyper 212 vein so you can overclock.