You have two ways to go.
1) Use any camcorder or camera (that happens to capture video as a convenience feature) that fits your budget and use video editing software on a computer to slow the video down. We don't know your budget, so making a recommendation is challenging. Keep in mind that high compression video (consumer grade AVCHD) and fast action do not get along.
2) Find a camera that captures video at a high frame rate. When that video is transferred to the computer, the video playback will be 30 fps and slow motion playback happens. At the low end, the Casio Exilim line has a couple that are at the higher end of that family.
Real high speed cameras typically do not capture video locally - they are connected to a computer where the video is stored.
Set the expectation: camcorders and cameras with small lenses and imaging chip cannot behave well under poor lighting conditions. Add in fast frame rate capture = need more light. Your indoor environment will likely require more light. This could be as simple as getting a couple of halogen worklights on tripods from the local hardware store.
If you watched the World Series a couple of weeks ago, please do not expect the same quality slow motion that was displayed. The Phantom cam (Vision Research) and lens set up used was in excess of $100,000.
Before a suggestion on software is made, we need to know what is available for you to use... and which way you choose to go relative to the camera/camcorder purchased. The real high speed cameras may come with their own software and have their own computer requirements specified.
What is a good camera to use to video high school baseball players swinging and pitching? Want to show the clips back in slow mo with great clarity for instructional purposes. Video will be taken inside during winter months. Any suggestions on fps or even on software to accompany a camera if that works? We are new to this and want to step up from our simple camera and youtube method. Thanks