While a TV is standard lounge-room fare, for a proper home theatre you should be looking at 80 inches or more. That's what home theatre is all about. And for that you need a projector.
Not just any old projector, but a home theatre projector. These are primarily marked by their resolution: full HD, or 1920x1080 pixels. Or, possibly, 4K projectors, with double the resolution in both dimensions: 3840x2160 pixels. But what else is there to consider?
At the moment there are three main technologies used for projectors: DLP, LCD and LCoS.
DLP uses a Digital Micromirror Device (DMD), or a chip covered by slightly more than 2 million microscopic mirrors. Each can move through an angle of up to 12 degrees to control where it is reflecting light.
Since there is only one panel to control the picture, the colours are shown in sequence. A rotating wheel with coloured transparent panels filters the light in sync with the moving mirrors on the DMD's surface.
All this sounds complicated and clunky, but in fact it delivers a significantly faster response, in terms of switching pixels on and off, than solid-state technology such as LCoS and LCD. It also means that the alignment between the three colours is perfect (subject to the quality of the projector's lens, of course). But in some implementations, the sequential delivery of colour can produce transient-coloured stripes with many viewers. This is called the "rainbow" effect.
Both LCD and LCoS projectors use three panels — one for each primary colour. With LCD the light passes through the panels, with LCoS it is reflected from the panel's surface. Because light passes through LCD pixels, the wiring has to go around the edges, meaning large inter-pixel boundaries. In earlier years this used to result in a "screen door" effect, but that has been eliminated in current full HD models.
A basic projector would have to have its position calculated very accurately with respect to the screen to ensure the picture ended up in the right place, at the right size. Modern projectors allow more flexibility. They can zoom their lenses to make the projected image bigger or smaller, and many have a "lens shift" feature, which allows you to adjust the direction in which the image is projected without trapezoidal distortion (which is what results from physically angling the projector).
These days all you really need is an HDMI connection. Many projectors still have legacy analog inputs, though. One of these has WirelessHD, and new cable-free HDMI connection.
Triggers can be useful for controlling other equipment, while many projectors have a good old-fashioned RS-232C socket. This is used by system integrators who can provide unified control over an entire home theatre system with one device.