Use image sequences. Otherwise Quicktime with PNG, JPEG or Animation compression are pretty much your only option. DNxHD could work, but some of that stuff is pretty flaky. Eitehr way, ProRes and other Apple-only stuff is out of the game here since there is no good and reliable way to encode it on a PC without jumping hoops via ffmpeg et al...
What I really need to know is how to use Adobe Media Encoder or After Effects Render on PC/Windows 8 to compress Footage into a small enough file size to be quickly transferred from one computer to another and into a codec that I can use to edit on Final Cut Pro 7 MacBook.
When you are working in a production pipeline you do not want to go for compressed file sizes, especially if you are color grading the final product. If your camera original is not ProRez then I would not transfer the files between systems, I'd spend a hundred bucks on a fast external hard drive and just connect the drive to the Mac for editing and to the PC for color grading. If you really want to spend time copying files from one system to another then you need all the information in the footage you can get so do what Mylenium suggested. I'd go for the Image Sequence and keep the bit depth up above 8bit. I have one more concern. It comes from this part of your question:
Now, as my new PC is more powerful than my MacBook my intention is to do the Color Correction and render on the PC. Next I want to use a local connection between the PC and Mac (Is already set up) to transfer the Color Corrected footage to my MacBook and complete a Final Cut pro 7 edit on that.
Color grading in normal production workflow is finalized after the project is edited. I always do mine after the final sound mix. I do set up an initial color grade for the footage, especially if it is shot LOG, but final color grading is always the last step for me and most pros that I know. If it were my workflow and I wanted to cut in FCP Pro I would cut the project first, then I would do the color grading. Color grading can be a slow process, but even if you are very fast at it, taking the time to color grade your original footage other than a general color profile setting is a terrible waste of time. If your shooting ratio is 3 or 4 to one then it's bad, if it's 8 to 10 to one, it's terrible, or, if you are like some of the new filmmakers I've seen struggling with their first production, your shooting ratio could be as high as 50 or even 100 to one.
I hope this helps.
If you use Go Pro Studio Premium ( formerly NeoCene by cineform), you can create cineform mov files --these are considered a digital intermediate format acceptable even in Hollywood :-)
I will automatically up sample a 4-2-0 color space like a Canon 5D Mark II, to a 4-2-2 color space, or 4-4-4, which will be much better for color grading than the original camera codec.
Both MC and PC are fine with the cineform mov's..people than use cineform and only a pc, tend to use the cineform avi rather than the mov wrapper, but in your case, the mov wrapper will work on both machines.....
But...you would want to do the color grading on the machine you will do the final work in for final render, as I don't know how easy it is to pass the database of color corrections from the codec level from one pc to the next....Cineform allows instantaneous color correction , rather than having to render the color correction--but this is computer/device specific , up until you render an output .
For all of my DSLR footage I started using Red Giant's Magic Bullet Grinder to produce a DI. It is now a legacy product but has been replaced with Red Giant - Products - BulletProof 1.2, a much more robust tool for digital film makers. I highly recommend this product to improve your workflow. It will save you more than the purchase price on your first project that is longer than 10 minutes.