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.