Regarding the monitor stuff:
DVI is the oldest, but that doesn't mean it's bad. DVI-D is digital only, and DVI-I is digtal
and analogue, although the only real use of the analogue signal is a DVI->VGA adapter. Single-link (rare now) only handles up to 1920×1200 @ 60Hz, which is barely above 1080p, dual-link enables resolutions of up to 2560×1600 @ 60Hz, which handles almost everything except 4k.
HDMI is
compatible with DVI, but extends the signalling to be able to do 2560×1600 @ 60Hz over a single link (as a result there's no such thing as dual-link HDMI) as well as carry audio. As it's compatible, the majority of DVI ports actually carry HDMI signals these days, making HDMI and DVI basically the same thing.
DisplayPort is the newest, and is
compatible with HDMI, and by extension DVI (if the port is "dual-mode", which is likely). The newest version of DisplayPort is somewhat insane, it enables resolutions of up to 5120×2880 (aka 5k) @ 60 Hz with monitors, or up to 8k (7680×4320) @ 60 Hz with TVs, or also stereoscopic 3d (or VR) @ 4k 60Hz (per eye, aka 120Hz).
Most displays (except 4k) are HDMI, so due to all the inter-compatibility you can use pretty much whichever cable and adapters you like and it will use a HDMI signal
(excepting VGA of course. Never use VGA with a digital monitor)