If you're okay with learning the basics of using a new operating system, I've heard that the Google Chromebook offerings were pretty solid, especially when it comes to your requirements. Due to almost all of your files being stored on Google's servers, your computer should boot very quickly and you should be able to do everything you need to almost immediately afterwards. Now, Google's Chromebook doesn't run EXE files (such as the Microsoft Office suite and most predominately-Windows programs) since it's not Windows, but if you'll just be using it for online browsing and creating documents, spreadsheets, etc., then it may interest you.
The lowest-price Chromebook is around $200, and you can find more information about different models and features over at this link: https://www.google.com/intl/en/chrome/devices/chromebooks.html
PS: The main reason I suggest a Chromebook is due to insignificance of storage and need for only basic programs, as well as protection against most forms of malware. Of course, you may not care to learn how to use another operating system or may need to use certain Windows programs, but it's definitely worth looking at if it'll fit your requirements and won't prove to be too much of a burden.