VGA is a strictly analog video-only signal system used mostly for computers to their monitors.
DVI is totally digital video only (originally) used a lot for connecting computer to monitor. Some "TV's" also accept this input. DVI cables do NOT carry audio in any form, so hooking up video this way usually means you use a separate cable to connect audio in whatever form to the sound output system.
HDMI also is digital on the video signals (in fact, electrically the digital video signals on HDMI and DVI are identical), but it also carries audio signals on the same cable. It is widely used for interconnections among computers, TV's, audio systems, DVD players, etc. Set up properly, you do NOT need separate audio connection cables when using HDMI. Some HDMI systems on "TV's" allow a second HDMI cable to be run from the TV to an audio system, thus passing the audio signals through the TV on to the audio system for better-quality reproduction.
If your computer has only a DVI output and no HDMI connector, an adapter can convert the DVI to an HDMI connector and give you the digital video part of the HDMI signals on a cable. However, the original DVI specs did not include audio so this adapter system does not address that issue. BUT some video cards, notably those based on ATI chips, include a feed of audio from the computer's audio system through the DVI output on otherwise-unused pins, and if you buy the correct adapter for this system you DO get both digital video and audio on the HDMI cable, conforming to the HDMI specs.
For OP, a standard HDMI cable is male-to-male and should do exactly what you need. You probably will not use VGA for anything - in fact, I don't know whether you even have a VGA output available on the computer you've ordered.