You can preserve most of your installed software like this:
Before you start your new install, open a terminal and type this

dpkg --get-selections "*" > Desktop/applications

Since you haven't got a separate /Home partition, make sure you include
Desktop in your backup (or anyway, make sure you include the file called
"applications" which the command has generated).

Once your new install is done, you'll need 1) to apply the latest
updates, then 2) to restore your backed-up /Home data, then 3) issue
these commands in a terminal:

sudo apt-get update
sudo dpkg --set-selections < Desktop/applications
sudo apt-get -u dselect-upgrade

The final command takes quite a while to run, but it's a lot easier than
doing it all manually.