Need to find out which parts to buy

Hello there. This looks like the 15-177 Pivot Shoe, which uses Series 152 Coil Balances. For each replacement coil spring you buy you have to choose a spring weight. This designates the weight the individual coil spring can support. Look for a stamp on the spring that indicates what to pick. If there is none, or you're unsure, just give me the exact weight of the window sash that these balances support, and I can calculate it for you. 

If your old housing is undamaged you can reuse it. Otherwise, see the 15-143, 15-144 and 15-145. These pieces 'sandwich' around each individual coil. Let me know if you have questions. 

You'll definitely want as precise as sash weight as you can manage. One method a lot of professionals use is to weigh yourself while you're holding the sash, then weigh yourself without it. If you subtract the difference, you'll get an accurate number.

Either way, you divide the sash weight by how many springs support it in total. In your case that would be 4. So if the sash is 18 pounds, you want one 4 pound and one 5 pound spring per side. If it's 19.4 pounds, you could use two 5 pound springs per side for a total of 20 pounds. That should be okay.

As for the hooks you mentioned, it sounds like you're referring to the pivot bar, but I'm not sure. I'll have to see a photo of the original removed from the window in order to find a match on our site. The 15-177 shoe is compatible with many, many different types.