Could someone please recommend a decent camera that when plugged into the HDMI out port won't show all of the menu and text from the camera screen on the TV screen in the overflow room?
Most pro-level gear includes some menu setting(s) to disable OSD (on-screen display) information (input name, input type, etc.). Depending on the unit you're look at, that may or may not be an option.
Or is there an easier/better way to accomplish this?
I doubt you will find a 100' long HDMI cable that can also be run in walls and/or plenum spaces (air ducts, above drop-ceilings, etc.). There are various extenders that allow you to transmit signal for hundreds of feet, depending on the end resolution you desire at the display. Many use Cat5-type cable, but there are also options that use fiber optic cable.
If you really want true HD video, I would look for a unit that uses DVI-D or HD-SDI/3G-SDI as its output. They are professional formats that are made to run the distance - and the converters can be usually used elsewhere if you decide to do something different with the setup.
Don't forget you'll also have to think about how audio is getting to the room, and whether or not it needs to be delayed to match the video on the monitor.