TeXShop equivalent on Windows

TeXShop does not run on Windows. So if you want to use the same editor on both machines you could use TeXworks which runs on both Mac and PC.

I too for the sake of compatibility stuck with TeXworks on both platforms when I started my ventures into LaTeX, but since then have moved to TeXShop on my mac. The initial move was due to the built in spell checker.

A very comprehensive list of editors/IDE's can be found at: