UEFI is something new, it kind of replaces the BIOS. It's used on new Computers that come most times with Windows 8. You don't have to worry about that.
32-bit will work in every case. If you can, you should use a 64-bit installation. It's faster and supports more (random access) memory. You can use up to between 3 to 4 GB of RAM with a 32-bit machine.
If it's an old computer it may support only 32-bit. Newer ones support mostly 64-bit (and 32-bit too). If you try to install a 64-bit Ubuntu on a 32-bit machine, it won't work, so you can just try if you want. If it does not work, try 32-bit Ubuntu. Your computer should tell you if you try to install 64-bit Ubuntu on a 32-bit computer.
Alternatively just look whether your windows XP installation is 32-bit or 64-bit. It should be visible somewhere in the "Workspace > Right-Click > Properties" (Names may be different since I did never use Windows in english.)
If you feel Ubuntu is too slow on your computer, or even the 32-bit version does not work correctly, please understand that Ubuntu is a modern system that is supposed to run on not too old computers. In this case, consider using these Ubuntu derivatives:
These are supposed to run smoothly on older computers and offer a different desktop experience (with better performance).