HDMI is really best for connecting a PC to an HDTV. Consequently, I’d go with a DVI cable. That’ll give you a pure digital signal (VGA is analog) and a much sharper picture at higher resolutions.

Whether you need a DisplayPort or an HDMI cable depends mainly on what you're connecting. DP cables are most frequently found in high-end computer setups, particularly gaming computer setups.This ...

The connection method does not matter, as long as the grounds are connected (HDMI cable, VGA cable, etc). I'm thinking that by using some kind of fiber optic HDMI extender, ...

Contrary to what continuum says (he's usually spot on, though), it's quite normal for a HDMI to VGA adapter to be fairly warm. Ballpark figure for a HDMI to VGA decoder is around 200 mA at 5 volts.

How to connect your PC to a projector. 1. Ensure both your laptop and your projector are powered off before connecting the two via the VGA cable, HDMI cable, and/or additional adapters.

Thunderbolt Gen 1 and 2 don’t support USB 3.1, Type C or even 3.0 for that matter. An adapter wouldn’t have fixed this problem. However, Apple is releasing Thunderbolt 3 later in 2015.