i would check to see what connectors you have before you go out and buy any cables.
a laptop with hdmi output would be easiest... but some laptops have vga or displayport
since most companies tend to use dell and keep them around for several years that may be the case... look what you have before you go buy.
it came up in search that the shortcut might be fn+f7 on dells.. another thing to keep in mind.
what changing the display mode does is set the monitor status from "laptop screen" to "laptop screen + external monitor copied desktop" to "laptop screen + external monitor extended desktop" to "external monitor only" and then back again. one of these modes should suffice (you can just page through them)
i havent had a laptop yet that automatically set itself to the mode.
i have used hdmi output on my personal laptop on my own television and in several hotels, provided they have a hdmi connection. the one thing you might need to adjust is "scaling" or the "overscan/underscan" options to fill the tv. sometimes by default the whole picture doesnt show and is stretched strange until you fix this. i've only had to do it once per tv i've used.