Cropping Tutorial, which should answer all your questions about aspect ratio and resolution and such. Yeah, it has numbers, but the pictures make it easier to understand. 
https://photography-on-the.net/forum/showthread.php?t=34567
Just remember that MPix probably wants 300 DPI. and that's a safe guess anyway. By the time you're done with the above tutorial you should easily be able to give them 4x6, 5x7, 8x10 - anything - at 300 DPI. It pretty easy if you give it 10 minutes.
Just re-read your entire post. Please realize that you camera takes pictures at a certain size. Like a 350D or 20D shoot at a 2:3 aspect ratio, which means that the long side (3) is 1.5 times as long as the short side (2). This works perfectly for a 4x6, but something like a 5x7 has the long side 1.4 times as long as the short side. You will have to crop, and you will have to lose some of the image when you do. There's nothing you can do about it.
Well, you could get custom 8x12 prints, or 6x9, or 7x10.5... But you'll have a very hard time finding paper or frames for those sizes. Yes, it can be done, but it's easier and cheaper just to go with the standard sizes.