LMCE is currently 0710 only. The 0810 version is in Alpha at this stage, and will go Beta shortly, however as you are new to LMCE, you should only use 0710.
There are 2 installation methods - CD and DVD. You only need to choose one, not both. Choose DVD - this is much faster (~ 40mins vs 2-3hrs for CDs) and more straightforward.
There are 2 versions, 64bit (AMD64, works on either AMD or Intel) and 32bit (i386, again works on both chips) - choose 32bit as 1) it is more stable and 2) 64bit will not get you significantly more speed with this type of workload.
You need to ensure that you have hardware that is compatible. Look for a motherboard that is compatible with Linux kernel 2.6.22-14 - this is the kernel that comes with Kubuntu 0710. The video chipset should be nVidia for simplicity. Chips in the 6200-7300 range are perfectly adequate, however something in the 8xxx and 9xxx series will also work and in due course will also give hardware acceleration of video (post 0810). Most new nVidia chipsets will require you to install the latest video drivers, use this guide to update them - http://wiki.linuxmce.org/index.php/Display_Drivers
The other important hardware considerations are compatible audio and network chipsets. Generally, if they have drivers for 0710/2.6.22-14 and the audio driver works with ALSA, you should be fine. When you find a mainboard, search the forums and wiki for these chipset numbers to see if there is any commentary on compatibility.
You need to understand the networking requirements for your core/hybrid machine, here - http://wiki.linuxmce.org/index.php/Network_Setup
When ready to install, you just ensure the BIOS is prepared to boot from DVD, put the DVD in and boot. You do not need to install any software at all beforehand, it is all on the DVD. It will ask you some questions about which disk to install on - NOTE: the installer will overrwrite all data and partitions on the disk you point it to.