Wow lots of questions..... and take a deep breath!
2.5 inch drives are based on laptop drives, they are physically smaller and don't require a separate mains power supply as they will be powered from the USB ports. 3.5 inch drives are based on desktop drives and are larger physically and will require a mains power supply.
For size, get as large as you can afford but there is not need for it to be larger than your internal hard drive (though you probably won't get one smaller than 250GB these days)
Which is recommended depends on if you want portable or not.... 2.5s are more portable than 3.5s
No you can not put your operating system on the EHD and you should not install any programs onto it either, you can only store your personal data files on it (music, films, pictures, documents etc etc)
and to be honest, brand isn't a huge concern for an EHD... look at Tescos, they are doing some good deals on EHDs at the moment.
http://direct.tesco.c...26&btnResultSort.y=10