I want to run Debian for some development in C++14, but I don't want to install it as a VMWare or use a Live CD. (Besides, Debian seems to need three DVD's to begin with.)
A Live USB doesn't work for me, as I want to keep all settings and files I save onto it.
How would I go about installing Debian 7.8.0 onto a USB 32GB USB3.0 stick from Windows 8.1?
Pen Drive Linux's Universal USB Installer will let you create bootable USB media. Is that what you are looking for or are you wanting to run Debian from the USB stick from within Windows?
You wouldn't need all 3 DVDs just to setup Debian. Downloading the netinst ISO would be enough just to get Debian running and installing additional software using apt-get afterwards. If you want to have a desktop environment, choose to download the KDE, LXDE or XFCE ISO. Then either burn that to a CD or write the image to a USB stick. Boot the installer and let it install Debian onto (another) USB stick. When booting your computer, choose to boot from USB and you should be fine. You can take that USB stick and go to every other computer and boot off it, as long as the architecture is compatible.
I just want to add to Dimblefeck's answer that Pen Drive Linux with Debian (among others) supports Persistent Storage, which means you can save settings and files to the Live USB stick without loosing them between sessions.
Another option is LiLi(LinuxLive) which has the same support but also allows you to boot the OS from Portable Virtual Box. There is an issue with using Persistent Storage from inside a virtual session, so consider it a tool for the occasions when you don't need to save any changes.
