Replacing Mac Mini Hard Drive with SSD, and New ML Install

Question

I have a mid-2011 Mac Mini, and it has been running very sluggish, even when there are multiple free GB of RAM and the processor is only at 10 to 20% of capacity. I ran TechTool Pro 6 to do a scan of the whole machine, and it didn't detect anything out of the ordinary.
At this point I am guessing that it's probably a software issue. I have tons of processes running in the background all the time, and have installed hundreds of programs over the last two years, so it could be anything number of things that are somehow messing up Mountain Lion.
So, I would like to replace the 500GB internal hard drive with a 120GB SSD Drive (Samsung 840 Series), and put a fresh install of Mountain Lion on the SSD, put the 500GB in an external enclosure, and see if that fixes the problem.
Can someone explain the best way for me to do this, in a step by step list?
I can figure out how to accomplish each step, I just need some overall guidance as to how I should approach the whole thing.
Thanks very much!
Some other notes:
I have a 3 TB hard drive that I can use to back up everything on the 500 GB hard drive, but I'm assuming that time machine isn't the best way to back everything up, since I won't be able to restore the machine on the 120GB drive that I want to boot from.
Normally, I would get the internal 500GB down to 100GB of data, and then clone it on the SSD, and make the swap, but I'm assuming that cloning the drive will potentially replicate the source of the slowness, so I'm assuming that isn't the best way to proceed.

Answer 1

Here is my opinion and steps I would perform.
Back up your system first.
Check the iFixit.com site for a guide of how to replace the drive. Review Steps 3 and 4 BEFORE you replace your drive.
If you have a USB thumb drive with the ML 10.8.3 installer, skip to step 6.
If you don't have a USB thumb drive with the ML 10.8.3 installer, download the OS X Recovery Disk Assistant and use a 1-4GB thumb drive to create a Recovery HD on the thumb drive you can boot from. Skip to step 6.
If you have neither of the above, after replacing the drive, restart into Internet Recovery by pressing/holding the Command+Option+R keys. Since you have a mid-2011, Internet Recovery will ONLY allow you to download and install Lion since that's what probably came preinstalled on your system.
After you replace your drive and you are booted into the OS X Utilities Menu from one of Steps 3-5, select Disk Utility and format your new drive as Mac OS Extended-Journaled with the GUID partition table.
Go back to the OS X Utilities Menu and select Reinstall Mac OS X.
After the download and install of OS X you can run through the setup creating your user account (same as you had on you old drive).
If you were able to install OS X ML, skip to step 11.
If you installed Lion, you will have to login to the App Store and download/install your purchase of ML.
Run Software Updates to bring your OS X up to date.
Now you can restore any data files and apps that will fit onto the new drive from Time Machine. Enter Time Machine and navigate to your last backup to view the /Applications folders and your user folders (e.g Documents, Downloads, Music, etc.).
For your email, you can open Finder then press the Option key to see your user Library folder in the list. Select it to open it then enter Time Machine again and navigate to your last backup so that your user Library folder is opened in Time Machine. Copy your Mail folder to your Desktop so you can copy it back to your current user Library.
I think that's it.