Since you're using Windows 8.x, it is fairly safe to assume that you can and should use a 64-Bit version of Ubuntu. If your computer is protected by UEFI Secure Boot, then you have no choice at all. You have to use 64-bit Ubuntu.
It seems to me that you might be new to Ubuntu. In that case, I recommend that you install the newest LTS (long-term support) of Ubuntu, which is 12.04LTS. You can download the iso for that here: http://releases.ubuntu.com/12.04.3/ubuntu-12.04.3-desktop-amd64.iso
If you want the newest release, even if you have to upgrade the OS in about 8 months, you can get Ubuntu 13.10 from here: http://releases.ubuntu.com/saucy/ubuntu-13.10-desktop-amd64.iso
Now, on the Windows-side, in order to make a USB memory stick bootable, you should download a program called Unetbootin. You can get it from here: http://unetbootin.sourceforge.net/unetbootin-windows-latest.exe
It's quite easy to use. You'll just select the iso-file and select the USB stick and that's mostly it.