Reddit mentions of Tektro R539 Dual Pivot Rear Brake Caliper - 47-57mm, Hex Nut, Silver

You'll definitely need a standard reach (vs. the new standard "short reach"). I made the mistake of not checking and had to run out and grab a new brake when I built my Steamroller. I have a Tektro R539.

My bike had the old style one too and I just drilled out the hole in the back of the fork to accommodate them. I couldn't really do that for the back one so I ended up using the front brake on the back and getting a really long nut to use the back one on the front http://problemsolversbike.com/products/sheldon_fender_nuts. The drilling took about a minute, just get a drill bit that's the same size as the nut (I think I used a 5/8 bit, but don't quote me on that). If that's too much work for you Tektro makes the old style mount ones too http://www.amazon.com/Tektro-R539-Pivot-Brake-Caliper/dp/B007QMIP2K but its $30 each for basically the same thing

With the wheelset you posted above, and assuming you'd be putting modern road tires on the wheels, no. You'd want this style of front brake and this style of rear brake.

Okay, so with $200, assuming I was doing the work:

Wrap handlebars - $11.53 (sweet dark red, cause the red on there looks awesome already)
Cheap 700c wheels from co-op - $20? (Talk with them about the gearing to see if the range is the same, or if you want tighter range or whatever, they probably have a few sets there with somewhat different gear ranges on the rear)
Saddle from co-op - $5-10
Tubes/tires - $45 (tires, tubes)
Derailleur cables - $7 (Shimano, here)
Brake cables - $10.39 (Shimano, here)
Brake levers - $22.53 (Tektro RL340)
Brakes - $62 - (Tektro 539 rear, front)
5-speed chain - 7.98 (here)

Then I'd try to get pedals and a cheap but aluminum quill stem, handlebars, and seatpost from the co-op. Depending on where you are, you may be able to get all for $20 or less. Functional new parts suggestions: (not guaranteed to fit. These have all sorts of different diameters over the years/models, so you need to know what you have/need. Handlebars, Seatpost, stem.)

These are pretty standard budget aftermarket brakes. The important thing is to measure from the mounting bolt to the plane of the brake pads on your current set in order to find the reach, then find replacements that fit. Looking at Giant Kronos pics, they look like pretty modern short-medium reach brakes.

Another option is to figure out what model of crank/derailleurs you have and find the brakes that were part of that groupset when they were sold new.