It is a good idea to explore automated testing, but it is difficult to create a system that will allow to you "press a few buttons or so to make sure everything's functioning as intended".  Automation is rarely a complete or easy replacement for manual testing.  Test automation requires a significant up-front investment and an ongoing maintenance cost.  It also requires skills that a manual tester will not necessarily have.

There are two ways to use Selenium: as a capture/replay tool or as a programming API.  Capture/replay tools never work very well (watch http://www.youtube.com/watch?feature=player_embedded&v=s_CUPs6xAWw for a good explanation) and I do not recommend using one.  Selenium is a decent programming API for writing UI tests, but it requires programming skills.

If you are interested in automated testing, I recommend hiring a programmer for your test team.  Instead of launching a grand project to replace all your manual testing with automation, I also recommend starting with a small pilot project, because you will learn things as you go. 

At this moment, there are 143 questions in this forum that mention the word "automation".  I suggest that you read at least some of them to familiarize yourself with some of the issues.