So Mrs. B. bought a MacBook Air because that’s what all stylish academicians use.
She needs to use it for presentations here and there, and it has only a Thunderbolt 2 port for video output. Dunno squatsky about TB, 1 or 2. (A little about DisplayPort.)
I’m big on HDMI and have found it to work wonderfully when it’s an available option. Since Apple doesn’t make a TB2-HDMI adapter (they offer DVI, VGA and Dual-Link DVI, and I assume the TB2 port can be connected to a DisplayPort as well with the right cable), but allows that third-party makers make such things…
…which is best for presentation use? DVI? or (specify maker) HDMI? With a TB2-DP cable as backup?
For video purposes, this port is a miniDisplayPort port.
Electrically, DVI and HDMI are the same, although HDMI can also carry sound and DVI can’t. DVI is still fairly common for connecting to LCD monitors, but it’s quickly being supplanted by DisplayPort and HDMI. For presentations, you need to connect to projectors or big TVs, which means either VGA or HDMI.
If you want to connect to a monitor, the best thing is a miniDisplayPort to (mini)DisplayPort cable and no adapters. Or an mDP to HDMI cable. Last option is the DVI adapter.
For presentations I’d get a VGA adapter as well as an HDMI adapter that accepts HDMI cables (rather than an mDP to HDMI cable that you need to plug into an HDMI socket). VGA because it’s still way too common but also HDMI because HDMI typically works better than VGA. VGA often means artificially low resolutions and even more autodetect trouble than HDMI.
(Yes, I have everything mentioned above…)
I’ve had some inconsistent experiences with mDP to HDMI adapters but that was years ago. (Having HDMI on my MacBook Pro is pretty sweet!) I’d assume that reputable ones will work without too much trouble as long as you don’t stress the connector too much and if not, get another one rather than worry preemptively.