Before going any further I would suggest a backup to an external drive.
Just because you may or may not have to end up doing a clean install.
Also I have come to find out that while updating over the current OS works most of the time and things work perfectly, sometimes you get little "gremlins" that are super hard to find and fix.
Generally a clean install makes life easier in the long run, think of updating your OS like updating your house with new paint and floors while leaving all of the furniture.
I'll just cover my usual process.
If you do not have tons of apps then this will be rather easy.
In Finder, on the lower left side, go down to devices. You should see the name of your hard drive listed. Click it and then users, which you should then see your Home Folder. The Icon will be of a house.
Unless you've saved files in specific places your Home Folder will house all of your Documents, Music, Downloads, Desktop files, Music, Pictures and Movies.
Just drag your home folder to a backup drive.
If you have an iCloud account, then your Mail, Contacts, Calendars, Safari Bookmarks will also be backed up.
If you decide to clean install just sign back into iCloud during the install process and all of this info should be downloaded back immediately.
You can find it in System Preferences->iCloud and just make sure you have all of the options you wanted saved to be checked.
Also you asked about your apps, if you have purchased all of them through the Mac App Store then all you have to do is sign back in after a clean install and go to the purchased tab and all of the apps tied to your account are available to you again.
If updating you must update to the most recent version of Lion and THEN update to Mountain Lion.
You do the update from within Lion
With a clean install you are starting fresh with ML.
It sounds like you have a good bootable USB copy of Lion ready to go so I'll start with a fresh install steps.
Make sure your USB is plugged into your computer and connect the power supply if you're on battery power.
You can hold down the power button at this point to shut the computer down because we aren't worried if OS X shuts down on it's own... we're starting fresh
Turn the machine back on and hold down the Option key immediately after the chime or grey screen appears, continue holding Option until the bootable drives appear and select your USB drive from the list.
Once in, select Disk Utility from the menu shown.(How I usually format) I select my hard drive from the left side menu in disk utility, not the named "Macintosh HD" partition but the HDD.
Click the partition tab on the right side and under partition layout, select 1 Partition ( or as many as you want ) and then name your drive whatever you would like. Format type should be the default OS Ext Journaled. Click Apply and it should be done within a few seconds.
Breathe deep, you just deleted everything, if it's backed up you're all good.
Close disk utility and Select to reinstall OSX and just follow along until the installation parts starts.
You can walk away and do laundry or make a sandwich at this point because it is going to take a while.
Once ML boots up for the first time it will ask you for a little bit of information such as your Apple ID and iCloud account so that it can pull all of your information and bookmarks.
Once on your desktop I would open two Finder Windows.
For me it makes it easier to drag and drop my files back to where they need to go.
If you have this Nifty little app called
Cinch, it basically gives your Mac the "Windows Snap" functionality. Where you can drag a window all the way to the left side of your screen and release and that window will take up the left half of your screen, same for the right, drag to the top of the screen and the window full screens without you having to manually resize the window.
You should basically be done at this point other than reinstalling apps.
You could also use an external as a Time Machine backup and do a fresh install from your USB drive then restore from the backup once you are in ML but every once in a while I've found those "gremlins" using this method as well.
Your best bet if you choose to take the plunge is do your fresh install, make sure you have everything installed the way you like it and then do a Time Machine backup from that point on.
This makes it less hectic if there is ever a next time and you know your backup is for the most part a clean backup.
