Hi Rea and Welcome to LQ.
Yes Mint could do what you want. So could Mythbuntu, Debian, Fedora etc.
Basically what you are referring to is distributions of Linux. Windows is made by and supplied Microsoft but Linux is supplied as an operating system with applications by many different groups/organisations. Red Hat , which you mention, isn't not free you have to purchase it. Ubuntu is, possibly, the most popular Linux distribution ever and it is free. Linux Mint is also very popular and it is also free. So we have 2 differences already.
When everything is said and done Mint (number/name) is a modified version of Ubuntu while Mint LMDE, Mint LXDE (and others named with just letters) are modified versions of Debian. What Mint does, with the Ubuntu variations, is make them more stable for general use by further modifying and adding their own little enhancements. The Mint (Debian) versions are no more stable than Debian but have visual enhancements to make it look prettier if you like Green.
Debian style Linux distributions use dpkg and apt or aptitude to manage packages. Red Hat style distributions (Red Hat, Fedora, Centos there are more) use RPM and other tools. Other distributions use different tools again.
So while yes each type of Linux is different they are all also similar in other ways because they use Desktop environments like Gnome, KDE, LXDE, XFCE, etc. The applications they use, OpenOffice or LibreOffice for example, are the same. It is often just the look and underlying (i.e. invisible) tools that are different. I would recommend you take a look at each ones home page for a general overview of each.
Last edited by k3lt01; 11-13-2011 at 09:59 AM.