A GTX 770 2GB model for $180 isn't worth it. You can get the newer
GTX 960 or R9 380 4GB models for a little bit more and
performance-wise they're slightly better. Some of those cards require rebates to come close to $190, though. However, those newer cards will benefit more from future driver updates while Kepler-based graphics cards like the GTX 770 are already on the wayside. Plus, that GTX 770 only has a 90 day warranty. The extra cost of a newer graphics card is much more worth it for the warranty and better performance.
Different graphics cards have different lengths. There are twin and triple fan versions of the GTX 980 Ti which range from 270~320mm in length, which is quite a difference from your Asus Strix GTX 970 which is 280mm long. If you're looking for compact models, I think MSI or EVGA's models of the GTX 980 Ti are better suited for you.
If you're not overclocking, a 600 watt power supply should be fine. What model and brand is it, though?
The recovery media is just something that boots up to a version of Acronis True Image that you can use without needing Windows to be installed. In case something happens to your installation of Windows and you still need to make some partition changes.
If you just do a normal installation of Windows 10, that won't allow you to dual boot with an existing installation of Windows 7. I have no idea what happened to your files, but you should refer to a
guide like this for specific steps in setting up a dual boot environment.