If I have an idea can I put it in my paper on my iPad or iPhone 4 with Pages (or some other app)
A plain text editor will create a document that any word processor on any platform (IBM or Mac) can open. How about a USB memory stick to transfer between machines? I know that works because I do it. Not sure if the stick needs a particular format.
Yes it does, leave the USB stick formatted to the FAT 32 it came with then both the Mac and PC can read it.
Not a solution for the iPad though.
Try DropBox. Install it on your iPad and your PC to then make your files accessible to both. Not a perfect solution though as you will be transferring and converting between Pages on the iPad and Word on Windows, which is an extra step and not perfect. At some point the conversion is not going to work perfectly and you will have problems.
Pages is not a substitute for Word and vice versa. As Yellowbox suggests, use a simpler Word Processing app. or Text Editor that will maintain basic formatting, and saves and opens in either .rtf, .txt or doc.