As a quick disclosure...Your first linux distro should depend on what you really want to accomplish/encounter. Ubuntu is an excellent distro for first time users because ease of use and compatability is great...even though it is debian.
I recommend synaptic package manager for your software/package management. It is a front end for apt. If you don't find it in the menu then open up a terminal, log in as root, update apt then install synaptic. Examples here.
These are the commands you will type in the terminal. but if there is a # sign in fron of my line it is just a note for you.
# the su command logs you in as superuser. It will require your password.
su
#the next command will update apt
apt-get update
#the next command will install synaptic
apt-get install synaptic
# the next command will start the program synaptic
synaptic
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While in synaptic you can view the packages in the top right box. Just highlight one and begin typing the name of the program you want....For example Firefox. When you see the firefox program click on the box next to it and select "install".
Then at the top of the program you will see a green checkmark labeled "apply"
Apply your changes and now firefox is installed. Do this for any programs you would like installed.
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If you want to have your debian machine running with all the nice multimedia bells and whistles a great program is Automatix. It will automatically install a lot of programs that can be challenging for a first time user.
have fun