I just installed CentOS 7 with Gnome desktop. In doing so, I created a root password, and added a user. Now I am logged in as the user. I like to install MariaDB server, PHP, and other software. To install these software, what are the implications of installing these software as root or as user?
You need to create a user and add that user to sudo. Depending on what flavor of Linux you're on it'll automatically add the user to sudo. If you get something like this user isn't on sudeoers list, just google it, you should be able to resolve it. Its best practice to use a user and sudo. Sudo basically means do something as a normal user with root permissions.
For example, to install php or mysql issue:
On Ubuntu sudo apt-get install lamp-server^ (this will install all lamp related software packages, it'll even prompt you to setup mysql server) all in one shot
On Redhat/Fedora/Centos sudo yum install php5, this, and that
This way when you need to alter software behavior, you'll only need to sudo something, to something if you know what I mean.
Well, to put it simply, installing as a root does not allow any of the user to alter the programs/applications installed.
In general, it is always recommended to install some sensitive applications(depending upon scenario based usage), as root.